Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 4^x-29*2^x+168=0
- Equation x+4/x-1-10/x^2-1=8
- Equation tan10x=cot5x
-
Equation x-x/11=50/11
- Express {x} in terms of y where:
- 8*x-7*y=-13
- 15*x-15*y=16
- 9*x+18*y=6
- (x^2+y^2-1)^3+x^2*y^3=0
-
Identical expressions
- x+ four /x- one - ten /x^ two - one = eight
- x plus 4 divide by x minus 1 minus 10 divide by x squared minus 1 equally 8
- x plus four divide by x minus one minus ten divide by x to the power of two minus one equally eight
- x+4/x-1-10/x2-1=8
- x+4/x-1-10/x²-1=8
- x+4/x-1-10/x to the power of 2-1=8
- x+4 divide by x-1-10 divide by x^2-1=8
-
Similar expressions
- x-4/x-1-10/x^2-1=8
- x+4/x-1+10/x^2-1=8
- x+4/x-1-10/x^2+1=8
- x+4/x+1-10/x^2-1=8
x+4/x-1-10/x^2-1=8 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
4 10
x + - - 1 - -- - 1 = 8
x 2
x
$$\left(\left(\left(x + \frac{4}{x}\right) - 1\right) - \frac{10}{x^{2}}\right) - 1 = 8$$
Rapid solution
[src]
_________________ / _________________ \
/ _______ | / _______ |
/ 955 \/ 25617 | ___ / 955 \/ 25617 |
3 / --- + --------- | \/ 3 *3 / --- + --------- ___ |
10 44 \/ 27 9 | \/ 27 9 44*\/ 3 |
x1 = -- - ------------------------ - ---------------------- + I*|- ---------------------------- + ------------------------|
3 _________________ 2 | 2 _________________|
/ _______ | / _______ |
/ 955 \/ 25617 | / 955 \/ 25617 |
9*3 / --- + --------- | 9*3 / --- + --------- |
\/ 27 9 \ \/ 27 9 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}{2} - \frac{44}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}} + \frac{10}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}{2} + \frac{44 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}\right)$$
_________________ / _________________ \
/ _______ | / _______ |
/ 955 \/ 25617 | ___ / 955 \/ 25617 |
3 / --- + --------- |\/ 3 *3 / --- + --------- ___ |
10 44 \/ 27 9 | \/ 27 9 44*\/ 3 |
x2 = -- - ------------------------ - ---------------------- + I*|---------------------------- - ------------------------|
3 _________________ 2 | 2 _________________|
/ _______ | / _______ |
/ 955 \/ 25617 | / 955 \/ 25617 |
9*3 / --- + --------- | 9*3 / --- + --------- |
\/ 27 9 \ \/ 27 9 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}{2} - \frac{44}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}} + \frac{10}{3} + i \left(- \frac{44 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}{2}\right)$$
_________________
/ _______
10 / 955 \/ 25617 88
x3 = -- + 3 / --- + --------- + ------------------------
3 \/ 27 9 _________________
/ _______
/ 955 \/ 25617
9*3 / --- + ---------
\/ 27 9
$$x_{3} = \frac{88}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}} + \frac{10}{3} + \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}$$
x3 = 88/(9*(sqrt(25617)/9 + 955/27)^(1/3)) + 10/3 + (sqrt(25617)/9 + 955/27)^(1/3)
Sum and product of roots
[src]
sum
_________________ / _________________ \ _________________ / _________________ \
/ _______ | / _______ | / _______ | / _______ |
/ 955 \/ 25617 | ___ / 955 \/ 25617 | / 955 \/ 25617 | ___ / 955 \/ 25617 | _________________
3 / --- + --------- | \/ 3 *3 / --- + --------- ___ | 3 / --- + --------- |\/ 3 *3 / --- + --------- ___ | / _______
10 44 \/ 27 9 | \/ 27 9 44*\/ 3 | 10 44 \/ 27 9 | \/ 27 9 44*\/ 3 | 10 / 955 \/ 25617 88
-- - ------------------------ - ---------------------- + I*|- ---------------------------- + ------------------------| + -- - ------------------------ - ---------------------- + I*|---------------------------- - ------------------------| + -- + 3 / --- + --------- + ------------------------
3 _________________ 2 | 2 _________________| 3 _________________ 2 | 2 _________________| 3 \/ 27 9 _________________
/ _______ | / _______ | / _______ | / _______ | / _______
/ 955 \/ 25617 | / 955 \/ 25617 | / 955 \/ 25617 | / 955 \/ 25617 | / 955 \/ 25617
9*3 / --- + --------- | 9*3 / --- + --------- | 9*3 / --- + --------- | 9*3 / --- + --------- | 9*3 / --- + ---------
\/ 27 9 \ \/ 27 9 / \/ 27 9 \ \/ 27 9 / \/ 27 9
$$\left(\frac{88}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}} + \frac{10}{3} + \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}{2} - \frac{44}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}} + \frac{10}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}{2} + \frac{44 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}{2} - \frac{44}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}} + \frac{10}{3} + i \left(- \frac{44 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}{2}\right)\right)\right)$$
=
/ _________________ \ / _________________ \
| / _______ | | / _______ |
| ___ / 955 \/ 25617 | | ___ / 955 \/ 25617 |
|\/ 3 *3 / --- + --------- ___ | | \/ 3 *3 / --- + --------- ___ |
| \/ 27 9 44*\/ 3 | | \/ 27 9 44*\/ 3 |
10 + I*|---------------------------- - ------------------------| + I*|- ---------------------------- + ------------------------|
| 2 _________________| | 2 _________________|
| / _______ | | / _______ |
| / 955 \/ 25617 | | / 955 \/ 25617 |
| 9*3 / --- + --------- | | 9*3 / --- + --------- |
\ \/ 27 9 / \ \/ 27 9 /
$$10 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}{2} + \frac{44 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}\right) + i \left(- \frac{44 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}{2}\right)$$
product
/ _________________ / _________________ \\ / _________________ / _________________ \\ | / _______ | / _______ || | / _______ | / _______ || | / 955 \/ 25617 | ___ / 955 \/ 25617 || | / 955 \/ 25617 | ___ / 955 \/ 25617 || / _________________ \ | 3 / --- + --------- | \/ 3 *3 / --- + --------- ___ || | 3 / --- + --------- |\/ 3 *3 / --- + --------- ___ || | / _______ | |10 44 \/ 27 9 | \/ 27 9 44*\/ 3 || |10 44 \/ 27 9 | \/ 27 9 44*\/ 3 || |10 / 955 \/ 25617 88 | |-- - ------------------------ - ---------------------- + I*|- ---------------------------- + ------------------------||*|-- - ------------------------ - ---------------------- + I*|---------------------------- - ------------------------||*|-- + 3 / --- + --------- + ------------------------| |3 _________________ 2 | 2 _________________|| |3 _________________ 2 | 2 _________________|| |3 \/ 27 9 _________________| | / _______ | / _______ || | / _______ | / _______ || | / _______ | | / 955 \/ 25617 | / 955 \/ 25617 || | / 955 \/ 25617 | / 955 \/ 25617 || | / 955 \/ 25617 | | 9*3 / --- + --------- | 9*3 / --- + --------- || | 9*3 / --- + --------- | 9*3 / --- + --------- || | 9*3 / --- + --------- | \ \/ 27 9 \ \/ 27 9 // \ \/ 27 9 \ \/ 27 9 // \ \/ 27 9 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}{2} - \frac{44}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}} + \frac{10}{3} + i \left(- \frac{44 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}{2} - \frac{44}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}} + \frac{10}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}{2} + \frac{44 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}}\right)\right) \left(\frac{88}{9 \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}} + \frac{10}{3} + \sqrt[3]{\frac{\sqrt{25617}}{9} + \frac{955}{27}}\right)$$
=
10
$$10$$
10
Numerical answer
[src]
x1 = 0.15310901832448 - 1.00406511142817*i
x2 = 0.15310901832448 + 1.00406511142817*i
x3 = 9.69378196335104
x3 = 9.69378196335104