Mister Exam
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How to use it?
- Equation:
- Equation 5*x^2-45=0
-
Equation x+4=-1
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Equation x-4=0
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Equation 16*x^3+8*x^2+x=0
- Express {x} in terms of y where:
- -16*x-10*y=4
- 7*x-19*y=17
- -19*x-15*y=15
- 20*x-9*y=-8
- Derivative of:
- 720
-
Identical expressions
- (x^ two -3x+ two)(x^ two -9x+ twenty)(x^ two -9x+ eighteen)= seven hundred and twenty
- (x squared minus 3x plus 2)(x squared minus 9x plus 20)(x squared minus 9x plus 18) equally 720
- (x to the power of two minus 3x plus two)(x to the power of two minus 9x plus twenty)(x to the power of two minus 9x plus eighteen) equally seven hundred and twenty
- (x2-3x+2)(x2-9x+20)(x2-9x+18)=720
- x2-3x+2x2-9x+20x2-9x+18=720
- (x²-3x+2)(x²-9x+20)(x²-9x+18)=720
- (x to the power of 2-3x+2)(x to the power of 2-9x+20)(x to the power of 2-9x+18)=720
- x^2-3x+2x^2-9x+20x^2-9x+18=720
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Similar expressions
- (x^2-3x+2)(x^2-9x+20)(x^2-9x-18)=720
- (x^2-3x+2)(x^2-9x+20)(x^2+9x+18)=720
- (x^2-3x-2)(x^2-9x+20)(x^2-9x+18)=720
- (x^2-3x+2)(x^2-9x-20)(x^2-9x+18)=720
- (x^2-3x+2)(x^2+9x+20)(x^2-9x+18)=720
- 2,41*(32,25+x)=5,13*x*2,72^(0,17*((x/2)-1))
- (x^2+3x+2)(x^2-9x+20)(x^2-9x+18)=720
(x^2-3x+2)(x^2-9x+20)(x^2-9x+18)=720 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ 2 \ / 2 \ / 2 \ \x - 3*x + 2/*\x - 9*x + 20/*\x - 9*x + 18/ = 720
$$\left(\left(x^{2} - 9 x\right) + 20\right) \left(\left(x^{2} - 3 x\right) + 2\right) \left(\left(x^{2} - 9 x\right) + 18\right) = 720$$
Rapid solution
[src]
x1 = 0
$$x_{1} = 0$$
x2 = 7
$$x_{2} = 7$$
/ / ____\\ / / ____\\
| |8*\/ 14 || | |8*\/ 14 ||
|atan|--------|| |atan|--------||
3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /|
3 *\/ 35 *sin|--------------| I*3 *\/ 35 *cos|--------------|
7 \ 2 / \ 2 /
x3 = - - ------------------------------- + ---------------------------------
2 2 2
$$x_{3} = - \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} + \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}$$
/ / ____\\ / / ____\\
| |8*\/ 14 || | |8*\/ 14 ||
|atan|--------|| |atan|--------||
3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /|
3 *\/ 35 *sin|--------------| I*3 *\/ 35 *cos|--------------|
7 \ 2 / \ 2 /
x4 = - + ------------------------------- - ---------------------------------
2 2 2
$$x_{4} = \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} - \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}$$
/ / ____\\ / / ____\\
| |8*\/ 14 || | |8*\/ 14 ||
|atan|--------|| |atan|--------||
3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /|
3 *\/ 35 *sin|--------------| I*3 *\/ 35 *cos|--------------|
7 \ 2 / \ 2 /
x5 = - - ------------------------------- - ---------------------------------
2 2 2
$$x_{5} = - \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} - \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}$$
/ / ____\\ / / ____\\
| |8*\/ 14 || | |8*\/ 14 ||
|atan|--------|| |atan|--------||
3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /|
3 *\/ 35 *sin|--------------| I*3 *\/ 35 *cos|--------------|
7 \ 2 / \ 2 /
x6 = - + ------------------------------- + ---------------------------------
2 2 2
$$x_{6} = \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} + \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}$$
x6 = 3^(3/4)*35^(1/4)*sin(atan(8*sqrt(14)/7)/2)/2 + 7/2 + 3^(3/4)*35^(1/4)*i*cos(atan(8*sqrt(14)/7)/2)/2
Sum and product of roots
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sum
/ / ____\\ / / ____\\ / / ____\\ / / ____\\ / / ____\\ / / ____\\ / / ____\\ / / ____\\
| |8*\/ 14 || | |8*\/ 14 || | |8*\/ 14 || | |8*\/ 14 || | |8*\/ 14 || | |8*\/ 14 || | |8*\/ 14 || | |8*\/ 14 ||
|atan|--------|| |atan|--------|| |atan|--------|| |atan|--------|| |atan|--------|| |atan|--------|| |atan|--------|| |atan|--------||
3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /|
3 *\/ 35 *sin|--------------| I*3 *\/ 35 *cos|--------------| 3 *\/ 35 *sin|--------------| I*3 *\/ 35 *cos|--------------| 3 *\/ 35 *sin|--------------| I*3 *\/ 35 *cos|--------------| 3 *\/ 35 *sin|--------------| I*3 *\/ 35 *cos|--------------|
7 \ 2 / \ 2 / 7 \ 2 / \ 2 / 7 \ 2 / \ 2 / 7 \ 2 / \ 2 /
7 + - - ------------------------------- + --------------------------------- + - + ------------------------------- - --------------------------------- + - - ------------------------------- - --------------------------------- + - + ------------------------------- + ---------------------------------
2 2 2 2 2 2 2 2 2 2 2 2
$$\left(\left(- \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} - \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right) + \left(\left(\frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} - \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right) + \left(7 + \left(- \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} + \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right)\right)\right)\right) + \left(\frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} + \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right)$$
=
21
$$21$$
product
/ / / ____\\ / / ____\\\ / / / ____\\ / / ____\\\ / / / ____\\ / / ____\\\ / / / ____\\ / / ____\\\
| | |8*\/ 14 || | |8*\/ 14 ||| | | |8*\/ 14 || | |8*\/ 14 ||| | | |8*\/ 14 || | |8*\/ 14 ||| | | |8*\/ 14 || | |8*\/ 14 |||
| |atan|--------|| |atan|--------||| | |atan|--------|| |atan|--------||| | |atan|--------|| |atan|--------||| | |atan|--------|| |atan|--------|||
| 3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /|| | 3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /|| | 3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /|| | 3/4 4 ____ | \ 7 /| 3/4 4 ____ | \ 7 /||
| 3 *\/ 35 *sin|--------------| I*3 *\/ 35 *cos|--------------|| | 3 *\/ 35 *sin|--------------| I*3 *\/ 35 *cos|--------------|| | 3 *\/ 35 *sin|--------------| I*3 *\/ 35 *cos|--------------|| | 3 *\/ 35 *sin|--------------| I*3 *\/ 35 *cos|--------------||
|7 \ 2 / \ 2 /| |7 \ 2 / \ 2 /| |7 \ 2 / \ 2 /| |7 \ 2 / \ 2 /|
0*7*|- - ------------------------------- + ---------------------------------|*|- + ------------------------------- - ---------------------------------|*|- - ------------------------------- - ---------------------------------|*|- + ------------------------------- + ---------------------------------|
\2 2 2 / \2 2 2 / \2 2 2 / \2 2 2 /
$$0 \cdot 7 \left(- \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} + \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right) \left(\frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} - \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right) \left(- \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} - \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right) \left(\frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} + \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right)$$
=
0
$$0$$
0
Numerical answer
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x1 = 5.22267424002185 - 2.17200518812337*i
x2 = 1.77732575997815 + 2.17200518812337*i
x3 = 5.22267424002185 + 2.17200518812337*i
x4 = 0.0
x5 = 1.77732575997815 - 2.17200518812337*i
x6 = 7.0
x6 = 7.0
The graph