Mister Exam
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How to use it?
- Equation:
-
Equation x^2+x=12
-
Equation 3x-2(3x-2)=19
-
Equation x^4=(x-56)^2
-
Equation (-2x+1)*(-2x-7)=0
- Express {x} in terms of y where:
- -7*x-13*y=-12
- 8*x+1*y=4
- 20*x-16*y=7
- -3*x+19*y=16
-
Identical expressions
- √ two *sin(x)-√ three /√7sin(x)= zero
- √2 multiply by sinus of (x) minus √3 divide by √7 sinus of (x) equally 0
- √ two multiply by sinus of (x) minus √ three divide by √7 sinus of (x) equally zero
- √2sin(x)-√3/√7sin(x)=0
- √2sinx-√3/√7sinx=0
- √2*sin(x)-√3/√7sin(x)=O
- √2*sin(x)-√3 divide by √7sin(x)=0
-
Similar expressions
- √2*sin(x)+√3/√7sin(x)=0
- √2*sinx-√3/√7sinx=0
√2*sin(x)-√3/√7sin(x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
___ \/ 3
\/ 2 *sin(x) - ------------ = 0
__________
\/ 7*sin(x)
$$\sqrt{2} \sin{\left(x \right)} - \frac{\sqrt{3}}{\sqrt{7 \sin{\left(x \right)}}} = 0$$
Detail solution
Given the equation
$$\sqrt{2} \sin{\left(x \right)} - \frac{\sqrt{3}}{\sqrt{7 \sin{\left(x \right)}}} = 0$$
transform
$$\sqrt{2} \sin{\left(x \right)} - \frac{\sqrt{21}}{7 \sqrt{\sin{\left(x \right)}}} = 0$$
$$\sqrt{2} \sin{\left(x \right)} - \frac{\sqrt{3}}{\sqrt{7 \sin{\left(x \right)}}} = 0$$
Do replacement
$$w = \sin{\left(x \right)}$$
Given the equation
$$\sqrt{2} w - \frac{\sqrt{21}}{7 \sqrt{w}} = 0$$
transform
$$w^{\frac{3}{2}} = \frac{\sqrt{42}}{14}$$
Because equation degree is equal to = 3/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2/3-th degree:
We get:
$$\left(w^{\frac{3}{2}}\right)^{\frac{2}{3}} = \left(\frac{\sqrt{42}}{14}\right)^{\frac{2}{3}}$$
or
$$w = \frac{\sqrt[3]{588}}{14}$$
Expand brackets in the right part
We get the answer: w = 588^(1/3)/14
All other 2 root(s) is the complex numbers.
do replacement:
$$z = w$$
then the equation will be the:
$$z^{\frac{3}{2}} = \frac{\sqrt{42}}{14}$$
Any complex number can presented so:
$$z = r e^{i p}$$
substitute to the equation
$$\left(r e^{i p}\right)^{\frac{3}{2}} = \frac{\sqrt{42}}{14}$$
where
$$r = \frac{\sqrt[3]{588}}{14}$$
- the magnitude of the complex number
Substitute r:
$$e^{\frac{3 i p}{2}} = 1$$
Using Euler’s formula, we find roots for p
$$i \sin{\left(\frac{3 p}{2} \right)} + \cos{\left(\frac{3 p}{2} \right)} = 1$$
so
$$\cos{\left(\frac{3 p}{2} \right)} = 1$$
and
$$\sin{\left(\frac{3 p}{2} \right)} = 0$$
then
$$p = \frac{4 \pi N}{3}$$
where N=0,1,2,3,...
Looping through the values of N and substituting p into the formula for z
Consequently, the solution will be for z:
$$z_{1} = \frac{14^{\frac{2}{3}} \sqrt[3]{3}}{14}$$
$$z_{2} = \left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2}$$
$$z_{3} = \left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2}$$
do backward replacement
$$z = w$$
$$w = z$$
The final answer:
$$w_{1} = \frac{14^{\frac{2}{3}} \sqrt[3]{3}}{14}$$
$$w_{2} = \left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2}$$
$$w_{3} = \left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2}$$
do backward replacement
$$\sin{\left(x \right)} = w$$
Given the equation
$$\sin{\left(x \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, where n - is a integer
substitute w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt[3]{588}}{14} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt[3]{588}}{14} \right)}$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt[3]{588}}{14} \right)} + \pi$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt[3]{588}}{14} \right)} + \pi$$
$$\sqrt{2} \sin{\left(x \right)} - \frac{\sqrt{3}}{\sqrt{7 \sin{\left(x \right)}}} = 0$$
transform
$$\sqrt{2} \sin{\left(x \right)} - \frac{\sqrt{21}}{7 \sqrt{\sin{\left(x \right)}}} = 0$$
$$\sqrt{2} \sin{\left(x \right)} - \frac{\sqrt{3}}{\sqrt{7 \sin{\left(x \right)}}} = 0$$
Do replacement
$$w = \sin{\left(x \right)}$$
Given the equation
$$\sqrt{2} w - \frac{\sqrt{21}}{7 \sqrt{w}} = 0$$
transform
$$w^{\frac{3}{2}} = \frac{\sqrt{42}}{14}$$
Because equation degree is equal to = 3/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2/3-th degree:
We get:
$$\left(w^{\frac{3}{2}}\right)^{\frac{2}{3}} = \left(\frac{\sqrt{42}}{14}\right)^{\frac{2}{3}}$$
or
$$w = \frac{\sqrt[3]{588}}{14}$$
Expand brackets in the right part
w = 588^1/3/14
We get the answer: w = 588^(1/3)/14
All other 2 root(s) is the complex numbers.
do replacement:
$$z = w$$
then the equation will be the:
$$z^{\frac{3}{2}} = \frac{\sqrt{42}}{14}$$
Any complex number can presented so:
$$z = r e^{i p}$$
substitute to the equation
$$\left(r e^{i p}\right)^{\frac{3}{2}} = \frac{\sqrt{42}}{14}$$
where
$$r = \frac{\sqrt[3]{588}}{14}$$
- the magnitude of the complex number
Substitute r:
$$e^{\frac{3 i p}{2}} = 1$$
Using Euler’s formula, we find roots for p
$$i \sin{\left(\frac{3 p}{2} \right)} + \cos{\left(\frac{3 p}{2} \right)} = 1$$
so
$$\cos{\left(\frac{3 p}{2} \right)} = 1$$
and
$$\sin{\left(\frac{3 p}{2} \right)} = 0$$
then
$$p = \frac{4 \pi N}{3}$$
where N=0,1,2,3,...
Looping through the values of N and substituting p into the formula for z
Consequently, the solution will be for z:
$$z_{1} = \frac{14^{\frac{2}{3}} \sqrt[3]{3}}{14}$$
$$z_{2} = \left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2}$$
$$z_{3} = \left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2}$$
do backward replacement
$$z = w$$
$$w = z$$
The final answer:
$$w_{1} = \frac{14^{\frac{2}{3}} \sqrt[3]{3}}{14}$$
$$w_{2} = \left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2}$$
$$w_{3} = \left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2}$$
do backward replacement
$$\sin{\left(x \right)} = w$$
Given the equation
$$\sin{\left(x \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, where n - is a integer
substitute w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt[3]{588}}{14} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt[3]{588}}{14} \right)}$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt[3]{588}}{14} \right)} + \pi$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt[3]{588}}{14} \right)} + \pi$$
Sum and product of roots
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sum
/ / 2\\ / / 2\\ / / 2\\ / / 2\\ / / 2\\ / / 2\\ / / 2\\ / / 2\\
/3 ___ 2/3\ /3 ___ 2/3\ | |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ ||
|\/ 3 *14 | |\/ 3 *14 | | || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | ||
pi - asin|-----------| + asin|-----------| + pi - re|asin||- ----------- - ------------| || - I*im|asin||- ----------- - ------------| || + pi - re|asin||- ----------- + ------------| || - I*im|asin||- ----------- + ------------| || + I*im|asin||- ----------- - ------------| || + re|asin||- ----------- - ------------| || + I*im|asin||- ----------- + ------------| || + re|asin||- ----------- + ------------| ||
\ 14 / \ 14 / \ \\ 28 28 / // \ \\ 28 28 / // \ \\ 28 28 / // \ \\ 28 28 / // \ \\ 28 28 / // \ \\ 28 28 / // \ \\ 28 28 / // \ \\ 28 28 / //
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)}\right) + \left(\left(\left(\left(\operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \sqrt[3]{3}}{14} \right)} + \left(\pi - \operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \sqrt[3]{3}}{14} \right)}\right)\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)}\right)\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)}\right)\right)$$
=
3*pi
$$3 \pi$$
product
/ / / 2\\ / / 2\\\ / / / 2\\ / / 2\\\ / / / 2\\ / / 2\\\ / / / 2\\ / / 2\\\ / /3 ___ 2/3\\ /3 ___ 2/3\ | | |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ ||| | | |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ ||| | | |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ ||| | | |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ ||| | |\/ 3 *14 || |\/ 3 *14 | | | || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | ||| | | || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | ||| | | || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | ||| | | || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | ||| |pi - asin|-----------||*asin|-----------|*|pi - re|asin||- ----------- - ------------| || - I*im|asin||- ----------- - ------------| |||*|pi - re|asin||- ----------- + ------------| || - I*im|asin||- ----------- + ------------| |||*|I*im|asin||- ----------- - ------------| || + re|asin||- ----------- - ------------| |||*|I*im|asin||- ----------- + ------------| || + re|asin||- ----------- + ------------| ||| \ \ 14 // \ 14 / \ \ \\ 28 28 / // \ \\ 28 28 / /// \ \ \\ 28 28 / // \ \\ 28 28 / /// \ \ \\ 28 28 / // \ \\ 28 28 / /// \ \ \\ 28 28 / // \ \\ 28 28 / ///
$$\left(\pi - \operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \sqrt[3]{3}}{14} \right)}\right) \operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \sqrt[3]{3}}{14} \right)} \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)}\right)$$
=
/ / / 2\\ / / 2\\\ / / / 2\\ / / 2\\\ / /3 ___ 2/3\\ / / / 2/3 /3 ___ 5/6\\\ / / 2/3 /3 ___ 5/6\\\\ | | | 2/3 /6 ___ 2/3\ || | | 2/3 /6 ___ 2/3\ ||| / / / 2/3 /3 ___ 5/6\\\ / / 2/3 /3 ___ 5/6\\\\ | | | 2/3 /6 ___ 2/3\ || | | 2/3 /6 ___ 2/3\ ||| /3 ___ 2/3\ | |\/ 3 *14 || | | |14 *\\/ 3 - I*3 /|| | |14 *\\/ 3 - I*3 /||| | | |14 *\\/ 3 - I*3 / || | |14 *\\/ 3 - I*3 / ||| | | |14 *\\/ 3 - I*3 /|| | |14 *\\/ 3 - I*3 /||| | | |14 *\\/ 3 - I*3 / || | |14 *\\/ 3 - I*3 / ||| |\/ 3 *14 | |pi - asin|-----------||*|I*im|asin|----------------------|| + re|asin|----------------------|||*|I*im|asin|-----------------------|| + re|asin|-----------------------|||*|pi + I*im|asin|----------------------|| + re|asin|----------------------|||*|-pi + I*im|asin|-----------------------|| + re|asin|-----------------------|||*asin|-----------| \ \ 14 // \ \ \ 28 // \ \ 28 /// \ \ \ 56 // \ \ 56 /// \ \ \ 28 // \ \ 28 /// \ \ \ 56 // \ \ 56 /// \ 14 /
$$\left(\pi - \operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \sqrt[3]{3}}{14} \right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \left(\sqrt[6]{3} - 3^{\frac{2}{3}} i\right)^{2}}{56} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \left(\sqrt[6]{3} - 3^{\frac{2}{3}} i\right)^{2}}{56} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \left(\sqrt[3]{3} - 3^{\frac{5}{6}} i\right)}{28} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \left(\sqrt[3]{3} - 3^{\frac{5}{6}} i\right)}{28} \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \left(\sqrt[6]{3} - 3^{\frac{2}{3}} i\right)^{2}}{56} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \left(\sqrt[6]{3} - 3^{\frac{2}{3}} i\right)^{2}}{56} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \left(\sqrt[3]{3} - 3^{\frac{5}{6}} i\right)}{28} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \left(\sqrt[3]{3} - 3^{\frac{5}{6}} i\right)}{28} \right)}\right)}\right) \operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \sqrt[3]{3}}{14} \right)}$$
(pi - asin(3^(1/3)*14^(2/3)/14))*(i*im(asin(14^(2/3)*(3^(1/3) - i*3^(5/6))/28)) + re(asin(14^(2/3)*(3^(1/3) - i*3^(5/6))/28)))*(i*im(asin(14^(2/3)*(3^(1/6) - i*3^(2/3))^2/56)) + re(asin(14^(2/3)*(3^(1/6) - i*3^(2/3))^2/56)))*(pi + i*im(asin(14^(2/3)*(3^(1/3) - i*3^(5/6))/28)) + re(asin(14^(2/3)*(3^(1/3) - i*3^(5/6))/28)))*(-pi + i*im(asin(14^(2/3)*(3^(1/6) - i*3^(2/3))^2/56)) + re(asin(14^(2/3)*(3^(1/6) - i*3^(2/3))^2/56)))*asin(3^(1/3)*14^(2/3)/14)
Rapid solution
[src]
/3 ___ 2/3\
|\/ 3 *14 |
x1 = pi - asin|-----------|
\ 14 /
$$x_{1} = \pi - \operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \sqrt[3]{3}}{14} \right)}$$
/3 ___ 2/3\
|\/ 3 *14 |
x2 = asin|-----------|
\ 14 /
$$x_{2} = \operatorname{asin}{\left(\frac{14^{\frac{2}{3}} \sqrt[3]{3}}{14} \right)}$$
/ / 2\\ / / 2\\
| |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ ||
| || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | ||
x3 = pi - re|asin||- ----------- - ------------| || - I*im|asin||- ----------- - ------------| ||
\ \\ 28 28 / // \ \\ 28 28 / //
$$x_{3} = - \operatorname{re}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)}$$
/ / 2\\ / / 2\\
| |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ ||
| || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | ||
x4 = pi - re|asin||- ----------- + ------------| || - I*im|asin||- ----------- + ------------| ||
\ \\ 28 28 / // \ \\ 28 28 / //
$$x_{4} = - \operatorname{re}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)}$$
/ / 2\\ / / 2\\
| |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ ||
| || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | ||
x5 = I*im|asin||- ----------- - ------------| || + re|asin||- ----------- - ------------| ||
\ \\ 28 28 / // \ \\ 28 28 / //
$$x_{5} = \operatorname{re}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} - \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)}$$
/ / 2\\ / / 2\\
| |/ 6 ___ 5/6 2/3 5/6\ || | |/ 6 ___ 5/6 2/3 5/6\ ||
| || \/ 3 *14 I*3 *14 | || | || \/ 3 *14 I*3 *14 | ||
x6 = I*im|asin||- ----------- + ------------| || + re|asin||- ----------- + ------------| ||
\ \\ 28 28 / // \ \\ 28 28 / //
$$x_{6} = \operatorname{re}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\left(- \frac{14^{\frac{5}{6}} \sqrt[6]{3}}{28} + \frac{14^{\frac{5}{6}} \cdot 3^{\frac{2}{3}} i}{28}\right)^{2} \right)}\right)}$$
x6 = re(asin((-14^(5/6)*3^(1/6)/28 + 14^(5/6)*3^(2/3)*i/28)^2)) + i*im(asin((-14^(5/6)*3^(1/6)/28 + 14^(5/6)*3^(2/3)*i/28)^2))
Numerical answer
[src]
x1 = 63.4733662619478
x2 = 13.2078838045111
x3 = -60.331773608358
x4 = 6.92469849733148
x5 = -49.6239692672848
x6 = -62.190339881644
x7 = 27.6328206921562
x8 = -24.4912280385665
x9 = -18.2080427313869
x10 = -91.7477001442559
x11 = -47.7654029939988
x12 = -79.1813295298967
x13 = 82.3229221834865
x14 = -99.8894517247215
x15 = 40.1991913065154
x16 = -10.0662911509213
x17 = 46.482376613695
x18 = 77.8983031495929
x19 = -30.774413345746
x20 = -35.1990323796396
x21 = 8.78326477061748
x22 = 84.1814884567725
x23 = 52.7655619208746
x24 = 21.3496353849767
x25 = 94.8892927978457
x26 = -93.6062664175419
x27 = -55.9071545744644
x28 = -28.91584707246
x29 = 76.0397368763069
x30 = 71.6151178424134
x31 = -74.7567104960031
x32 = 38.3406250332294
x33 = 33.9160059993358
x34 = 2.5000794634379
x35 = 96.7478590711317
x36 = -37.0575986529256
x37 = 19.4910691116907
x38 = -85.4645148370763
x39 = -5.64167211702769
x40 = 44.623810340409
x41 = -87.3230811103623
x42 = 50.9069956475886
x43 = -68.4735251888236
x44 = 69.7565515691274
x45 = -81.0398958031827
x46 = -22.6326617652804
x47 = -41.4822176868192
x48 = 90.4646737639521
x49 = 32.0574397260498
x50 = 134.446970914209
x51 = -54.0485883011784
x52 = -43.3407839601052
x53 = 101.172478105025
x54 = -11.9248574242073
x55 = -3.78310584374169
x56 = -72.8981442227171
x57 = 59.0487472280542
x58 = 65.3319325352338
x59 = 57.1901809547682
x60 = 25.7742544188702
x61 = 15.0664500777971
x62 = 88.6061074906661
x63 = -66.6149589155376
x64 = -98.0308854514355
x65 = -16.3494764581009
x65 = -16.3494764581009