Mister Exam
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- Equation:
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Equation x^2-11*x+28=0
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Equation 0*x=3
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Equation 8,4(y-17,9)=4,2
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Identical expressions
- one /(x- three)^ two - three /x- three + four = zero
- 1 divide by (x minus 3) squared minus 3 divide by x minus 3 plus 4 equally 0
- one divide by (x minus three) to the power of two minus three divide by x minus three plus four equally zero
- 1/(x-3)2-3/x-3+4=0
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- 1/x-3^2-3/x-3+4=0
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- 1 divide by (x-3)^2-3 divide by x-3+4=0
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Similar expressions
- 1/(x+3)^2-3/x-3+4=0
- 1/(x-3)^2-3/x+3+4=0
- 1/(x-3)^2+3/x-3+4=0
- 1/(x-3)^2-3/x-3-4=0
1/(x-3)^2-3/x-3+4=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
1 3
-------- - - - 3 + 4 = 0
2 x
(x - 3)
$$\left(\left(\frac{1}{\left(x - 3\right)^{2}} - \frac{3}{x}\right) - 3\right) + 4 = 0$$
Sum and product of roots
[src]
sum
________________ / ________________\ ________________ / ________________\ ________________
/ _____ | / _____ | / _____ | / _____ | / _____
/ 81 3*\/ 741 | ___ / 81 3*\/ 741 | / 81 3*\/ 741 | ___ / 81 3*\/ 741 | / 81 3*\/ 741
3 / -- + --------- | ___ \/ 3 *3 / -- + --------- | 3 / -- + --------- | ___ \/ 3 *3 / -- + --------- | 3 / -- + ---------
1 \/ 2 2 | \/ 3 \/ 2 2 | 1 \/ 2 2 | \/ 3 \/ 2 2 | 1 \/ 2 2
3 - ----------------------- + --------------------- + I*|----------------------- + ---------------------------| + 3 - ----------------------- + --------------------- + I*|- ----------------------- - ---------------------------| + 3 + --------------------- - ---------------------
________________ 6 | ________________ 6 | ________________ 6 | ________________ 6 | ________________ 3
/ _____ | / _____ | / _____ | / _____ | / _____
/ 81 3*\/ 741 | / 81 3*\/ 741 | / 81 3*\/ 741 | / 81 3*\/ 741 | / 81 3*\/ 741
2*3 / -- + --------- |2*3 / -- + --------- | 2*3 / -- + --------- | 2*3 / -- + --------- | 3 / -- + ---------
\/ 2 2 \ \/ 2 2 / \/ 2 2 \ \/ 2 2 / \/ 2 2
$$\left(- \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{3} + \frac{1}{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + 3\right) + \left(\left(- \frac{1}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} + 3 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} - \frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}\right)\right) + \left(- \frac{1}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} + 3 + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6}\right)\right)\right)$$
=
/ ________________\ / ________________\
| / _____ | | / _____ |
| ___ / 81 3*\/ 741 | | ___ / 81 3*\/ 741 |
| ___ \/ 3 *3 / -- + --------- | | ___ \/ 3 *3 / -- + --------- |
| \/ 3 \/ 2 2 | | \/ 3 \/ 2 2 |
9 + I*|----------------------- + ---------------------------| + I*|- ----------------------- - ---------------------------|
| ________________ 6 | | ________________ 6 |
| / _____ | | / _____ |
| / 81 3*\/ 741 | | / 81 3*\/ 741 |
|2*3 / -- + --------- | | 2*3 / -- + --------- |
\ \/ 2 2 / \ \/ 2 2 /
$$9 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} - \frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}\right) + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6}\right)$$
product
/ ________________ / ________________\\ / ________________ / ________________\\ / ________________\ | / _____ | / _____ || | / _____ | / _____ || | / _____ | | / 81 3*\/ 741 | ___ / 81 3*\/ 741 || | / 81 3*\/ 741 | ___ / 81 3*\/ 741 || | / 81 3*\/ 741 | | 3 / -- + --------- | ___ \/ 3 *3 / -- + --------- || | 3 / -- + --------- | ___ \/ 3 *3 / -- + --------- || | 3 / -- + --------- | | 1 \/ 2 2 | \/ 3 \/ 2 2 || | 1 \/ 2 2 | \/ 3 \/ 2 2 || | 1 \/ 2 2 | |3 - ----------------------- + --------------------- + I*|----------------------- + ---------------------------||*|3 - ----------------------- + --------------------- + I*|- ----------------------- - ---------------------------||*|3 + --------------------- - ---------------------| | ________________ 6 | ________________ 6 || | ________________ 6 | ________________ 6 || | ________________ 3 | | / _____ | / _____ || | / _____ | / _____ || | / _____ | | / 81 3*\/ 741 | / 81 3*\/ 741 || | / 81 3*\/ 741 | / 81 3*\/ 741 || | / 81 3*\/ 741 | | 2*3 / -- + --------- |2*3 / -- + --------- || | 2*3 / -- + --------- | 2*3 / -- + --------- || | 3 / -- + --------- | \ \/ 2 2 \ \/ 2 2 // \ \/ 2 2 \ \/ 2 2 // \ \/ 2 2 /
$$\left(- \frac{1}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} + 3 + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6}\right)\right) \left(- \frac{1}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} + 3 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} - \frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{3} + \frac{1}{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + 3\right)$$
=
__________________ ________________ __________________ 2/3 ________________ 2/3
3 / _____ 2/3 2/3 2/3 3 / _____ _____ 3 / _____ 3 ___ _____ / _____\ 2/3 _____ 3 / _____ 3 ___ 6 ___ _____ / _____\
747*\/ 324 + 12*\/ 741 3 ___ / _____\ 3 ____ / _____\ 747*2 *\/ 81 + 3*\/ 741 83*\/ 741 *\/ 324 + 12*\/ 741 7*\/ 2 *\/ 741 *\81 + 3*\/ 741 / 83*2 *\/ 741 *\/ 81 + 3*\/ 741 7*\/ 2 *\/ 3 *\/ 247 *\27 + \/ 741 /
27 + ------------------------- - 7*\/ 2 *\81 + 3*\/ 741 / + 7*\/ 18 *\27 + \/ 741 / - ---------------------------- - -------------------------------- + ----------------------------------- + ----------------------------------- - ---------------------------------------
8 8 24 27 24 9
$$- \frac{83 \sqrt{741} \sqrt[3]{324 + 12 \sqrt{741}}}{24} - \frac{747 \cdot 2^{\frac{2}{3}} \sqrt[3]{81 + 3 \sqrt{741}}}{8} - \frac{7 \sqrt[3]{2} \sqrt{247} \sqrt[6]{3} \left(27 + \sqrt{741}\right)^{\frac{2}{3}}}{9} - 7 \sqrt[3]{2} \left(81 + 3 \sqrt{741}\right)^{\frac{2}{3}} + 27 + 7 \sqrt[3]{18} \left(27 + \sqrt{741}\right)^{\frac{2}{3}} + \frac{7 \sqrt[3]{2} \sqrt{741} \left(81 + 3 \sqrt{741}\right)^{\frac{2}{3}}}{27} + \frac{747 \sqrt[3]{324 + 12 \sqrt{741}}}{8} + \frac{83 \cdot 2^{\frac{2}{3}} \sqrt{741} \sqrt[3]{81 + 3 \sqrt{741}}}{24}$$
27 + 747*(324 + 12*sqrt(741))^(1/3)/8 - 7*2^(1/3)*(81 + 3*sqrt(741))^(2/3) + 7*18^(1/3)*(27 + sqrt(741))^(2/3) - 747*2^(2/3)*(81 + 3*sqrt(741))^(1/3)/8 - 83*sqrt(741)*(324 + 12*sqrt(741))^(1/3)/24 + 7*2^(1/3)*sqrt(741)*(81 + 3*sqrt(741))^(2/3)/27 + 83*2^(2/3)*sqrt(741)*(81 + 3*sqrt(741))^(1/3)/24 - 7*2^(1/3)*3^(1/6)*sqrt(247)*(27 + sqrt(741))^(2/3)/9
Rapid solution
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________________ / ________________\
/ _____ | / _____ |
/ 81 3*\/ 741 | ___ / 81 3*\/ 741 |
3 / -- + --------- | ___ \/ 3 *3 / -- + --------- |
1 \/ 2 2 | \/ 3 \/ 2 2 |
x1 = 3 - ----------------------- + --------------------- + I*|----------------------- + ---------------------------|
________________ 6 | ________________ 6 |
/ _____ | / _____ |
/ 81 3*\/ 741 | / 81 3*\/ 741 |
2*3 / -- + --------- |2*3 / -- + --------- |
\/ 2 2 \ \/ 2 2 /
$$x_{1} = - \frac{1}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} + 3 + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6}\right)$$
________________ / ________________\
/ _____ | / _____ |
/ 81 3*\/ 741 | ___ / 81 3*\/ 741 |
3 / -- + --------- | ___ \/ 3 *3 / -- + --------- |
1 \/ 2 2 | \/ 3 \/ 2 2 |
x2 = 3 - ----------------------- + --------------------- + I*|- ----------------------- - ---------------------------|
________________ 6 | ________________ 6 |
/ _____ | / _____ |
/ 81 3*\/ 741 | / 81 3*\/ 741 |
2*3 / -- + --------- | 2*3 / -- + --------- |
\/ 2 2 \ \/ 2 2 /
$$x_{2} = - \frac{1}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} + 3 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} - \frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}\right)$$
________________
/ _____
/ 81 3*\/ 741
3 / -- + ---------
1 \/ 2 2
x3 = 3 + --------------------- - ---------------------
________________ 3
/ _____
/ 81 3*\/ 741
3 / -- + ---------
\/ 2 2
$$x_{3} = - \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{3} + \frac{1}{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + 3$$
x3 = -(81/2 + 3*sqrt(741)/2)^(1/3)/3 + (81/2 + 3*sqrt(741)/2)^(-1/3) + 3
Numerical answer
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x1 = 3.60670583138111 + 1.45061224918844*i
x2 = 3.60670583138111 - 1.45061224918844*i
x3 = 1.78658833723777
x3 = 1.78658833723777