Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation x-y=7
-
Equation 1/(x+6)=2
-
Equation (x-4)^2-x^2=0
-
Equation 6/(x+5)=-5
- Express {x} in terms of y where:
- 7*x-1*y=-7
- 10*x-15*y=16
- -14*x-12*y=5
- 13*x-12*y=19
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Identical expressions
- (x- six)^ three = sixteen (x+ six)
- (x minus 6) cubed equally 16(x plus 6)
- (x minus six) to the power of three equally sixteen (x plus six)
- (x-6)3=16(x+6)
- x-63=16x+6
- (x-6)³=16(x+6)
- (x-6) to the power of 3=16(x+6)
- x-6^3=16x+6
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Similar expressions
- 16x+64=-x^2
- x^2-16x+63=0
- 20x-10=12(16x+6)-10x
- x^2-16*x+63=0
- (x-6)^3=16(x-6)
- (x+6)^3=16(x+6)
(x-6)^3=16(x+6) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Sum and product of roots
[src]
sum
________________ / ________________ \ ________________ / ________________ \ ________________
/ _____ | / _____ ___ | / _____ | / _____ ___ | / _____
/ 4*\/ 717 4 | ___ / 4*\/ 717 4*\/ 3 | / 4*\/ 717 4 | ___ / 4*\/ 717 4*\/ 3 | / 4*\/ 717 8
6 - 3 / 12 + --------- - ----------------------- + I*|- \/ 3 *3 / 12 + --------- + -----------------------| + 6 - 3 / 12 + --------- - ----------------------- + I*|\/ 3 *3 / 12 + --------- - -----------------------| + 6 + 2*3 / 12 + --------- + -----------------------
\/ 9 ________________ | \/ 9 ________________| \/ 9 ________________ | \/ 9 ________________| \/ 9 ________________
/ _____ | / _____ | / _____ | / _____ | / _____
/ 4*\/ 717 | / 4*\/ 717 | / 4*\/ 717 | / 4*\/ 717 | / 4*\/ 717
3*3 / 12 + --------- | 3*3 / 12 + --------- | 3*3 / 12 + --------- | 3*3 / 12 + --------- | 3*3 / 12 + ---------
\/ 9 \ \/ 9 / \/ 9 \ \/ 9 / \/ 9
$$\left(\frac{8}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}} + 2 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12} + 6\right) + \left(\left(- \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12} - \frac{4}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}} + 6 + i \left(- \sqrt{3} \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12} + \frac{4 \sqrt{3}}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}}\right)\right) + \left(- \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12} - \frac{4}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}} + 6 + i \left(- \frac{4 \sqrt{3}}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}} + \sqrt{3} \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}\right)\right)\right)$$
=
/ ________________ \ / ________________ \
| / _____ ___ | | / _____ ___ |
| ___ / 4*\/ 717 4*\/ 3 | | ___ / 4*\/ 717 4*\/ 3 |
18 + I*|\/ 3 *3 / 12 + --------- - -----------------------| + I*|- \/ 3 *3 / 12 + --------- + -----------------------|
| \/ 9 ________________| | \/ 9 ________________|
| / _____ | | / _____ |
| / 4*\/ 717 | | / 4*\/ 717 |
| 3*3 / 12 + --------- | | 3*3 / 12 + --------- |
\ \/ 9 / \ \/ 9 /
$$18 + i \left(- \sqrt{3} \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12} + \frac{4 \sqrt{3}}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}}\right) + i \left(- \frac{4 \sqrt{3}}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}} + \sqrt{3} \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}\right)$$
product
/ ________________ / ________________ \\ / ________________ / ________________ \\ / ________________ \ | / _____ | / _____ ___ || | / _____ | / _____ ___ || | / _____ | | / 4*\/ 717 4 | ___ / 4*\/ 717 4*\/ 3 || | / 4*\/ 717 4 | ___ / 4*\/ 717 4*\/ 3 || | / 4*\/ 717 8 | |6 - 3 / 12 + --------- - ----------------------- + I*|- \/ 3 *3 / 12 + --------- + -----------------------||*|6 - 3 / 12 + --------- - ----------------------- + I*|\/ 3 *3 / 12 + --------- - -----------------------||*|6 + 2*3 / 12 + --------- + -----------------------| | \/ 9 ________________ | \/ 9 ________________|| | \/ 9 ________________ | \/ 9 ________________|| | \/ 9 ________________| | / _____ | / _____ || | / _____ | / _____ || | / _____ | | / 4*\/ 717 | / 4*\/ 717 || | / 4*\/ 717 | / 4*\/ 717 || | / 4*\/ 717 | | 3*3 / 12 + --------- | 3*3 / 12 + --------- || | 3*3 / 12 + --------- | 3*3 / 12 + --------- || | 3*3 / 12 + --------- | \ \/ 9 \ \/ 9 // \ \/ 9 \ \/ 9 // \ \/ 9 /
$$\left(- \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12} - \frac{4}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}} + 6 + i \left(- \frac{4 \sqrt{3}}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}} + \sqrt{3} \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}\right)\right) \left(- \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12} - \frac{4}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}} + 6 + i \left(- \sqrt{3} \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12} + \frac{4 \sqrt{3}}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}}\right)\right) \left(\frac{8}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}} + 2 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12} + 6\right)$$
=
__________________ 2/3 ________________ 2/3
__________________ ________________ 2/3 2/3 _____ 3 / _____ 3 ___ _____ / _____\ 2/3 _____ 3 / _____ 3 ___ 6 ___ _____ / _____\
3 / _____ 2/3 3 / _____ 3 ____ / _____\ 3 ___ / _____\ 154*\/ 717 *\/ 324 + 12*\/ 717 92*\/ 2 *\/ 717 *\81 + 3*\/ 717 / 154*2 *\/ 717 *\/ 81 + 3*\/ 717 92*\/ 2 *\/ 3 *\/ 239 *\27 + \/ 717 /
312 + 1386*\/ 324 + 12*\/ 717 - 1386*2 *\/ 81 + 3*\/ 717 - 92*\/ 18 *\27 + \/ 717 / + 92*\/ 2 *\81 + 3*\/ 717 / - --------------------------------- - ------------------------------------ + ------------------------------------ + ----------------------------------------
3 27 3 9
$$- 1386 \cdot 2^{\frac{2}{3}} \sqrt[3]{3 \sqrt{717} + 81} - \frac{154 \sqrt{717} \sqrt[3]{12 \sqrt{717} + 324}}{3} - 92 \sqrt[3]{18} \left(\sqrt{717} + 27\right)^{\frac{2}{3}} - \frac{92 \sqrt[3]{2} \sqrt{717} \left(3 \sqrt{717} + 81\right)^{\frac{2}{3}}}{27} + 312 + \frac{92 \sqrt[3]{2} \sqrt{239} \sqrt[6]{3} \left(\sqrt{717} + 27\right)^{\frac{2}{3}}}{9} + 92 \sqrt[3]{2} \left(3 \sqrt{717} + 81\right)^{\frac{2}{3}} + \frac{154 \cdot 2^{\frac{2}{3}} \sqrt{717} \sqrt[3]{3 \sqrt{717} + 81}}{3} + 1386 \sqrt[3]{12 \sqrt{717} + 324}$$
312 + 1386*(324 + 12*sqrt(717))^(1/3) - 1386*2^(2/3)*(81 + 3*sqrt(717))^(1/3) - 92*18^(1/3)*(27 + sqrt(717))^(2/3) + 92*2^(1/3)*(81 + 3*sqrt(717))^(2/3) - 154*sqrt(717)*(324 + 12*sqrt(717))^(1/3)/3 - 92*2^(1/3)*sqrt(717)*(81 + 3*sqrt(717))^(2/3)/27 + 154*2^(2/3)*sqrt(717)*(81 + 3*sqrt(717))^(1/3)/3 + 92*2^(1/3)*3^(1/6)*sqrt(239)*(27 + sqrt(717))^(2/3)/9
Rapid solution
[src]
________________ / ________________ \
/ _____ | / _____ ___ |
/ 4*\/ 717 4 | ___ / 4*\/ 717 4*\/ 3 |
x1 = 6 - 3 / 12 + --------- - ----------------------- + I*|- \/ 3 *3 / 12 + --------- + -----------------------|
\/ 9 ________________ | \/ 9 ________________|
/ _____ | / _____ |
/ 4*\/ 717 | / 4*\/ 717 |
3*3 / 12 + --------- | 3*3 / 12 + --------- |
\/ 9 \ \/ 9 /
$$x_{1} = - \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12} - \frac{4}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}} + 6 + i \left(- \sqrt{3} \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12} + \frac{4 \sqrt{3}}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}}\right)$$
________________ / ________________ \
/ _____ | / _____ ___ |
/ 4*\/ 717 4 | ___ / 4*\/ 717 4*\/ 3 |
x2 = 6 - 3 / 12 + --------- - ----------------------- + I*|\/ 3 *3 / 12 + --------- - -----------------------|
\/ 9 ________________ | \/ 9 ________________|
/ _____ | / _____ |
/ 4*\/ 717 | / 4*\/ 717 |
3*3 / 12 + --------- | 3*3 / 12 + --------- |
\/ 9 \ \/ 9 /
$$x_{2} = - \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12} - \frac{4}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}} + 6 + i \left(- \frac{4 \sqrt{3}}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}} + \sqrt{3} \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}\right)$$
________________
/ _____
/ 4*\/ 717 8
x3 = 6 + 2*3 / 12 + --------- + -----------------------
\/ 9 ________________
/ _____
/ 4*\/ 717
3*3 / 12 + ---------
\/ 9
$$x_{3} = \frac{8}{3 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12}} + 2 \sqrt[3]{\frac{4 \sqrt{717}}{9} + 12} + 6$$
x3 = 8/(3*(4*sqrt(717)/9 + 12)^(1/3)) + 2*(4*sqrt(717)/9 + 12)^(1/3) + 6
Numerical answer
[src]
x1 = 2.65660023668568 - 4.18747727539993*i
x2 = 2.65660023668568 + 4.18747727539993*i
x3 = 12.6867995266286
x3 = 12.6867995266286