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Equation:
Equation 5x^2-125=0
Equation 3x²-27=0
Equation sqrt^4(17x^2-16)=x
Equation (X+3)/5=6+(x/2)
Express {x} in terms of y where:
sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
10*x-1*y=10
15*x-17*y=19
9*x-8*y=6
Identical expressions
sqrt^ four (17x^ two - sixteen)=x
square root of to the power of 4(17x squared minus 16) equally x
square root of to the power of four (17x to the power of two minus sixteen) equally x
√^4(17x^2-16)=x
sqrt4(17x2-16)=x
sqrt417x2-16=x
sqrt⁴(17x²-16)=x
sqrt to the power of 4(17x to the power of 2-16)=x
sqrt^417x^2-16=x
Similar expressions
sqrt^4(17x^2+16)=x

sqrt^4(17x^2-16)=x equation

The teacher will be very surprised to see your correct solution 😉

The solution

You have entered [src]

               4    
   ____________     
  /     2           
\/  17*x  - 16   = x

$$\left(\sqrt{17 x^{2} - 16}\right)^{4} = x$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

x1 = 1

$$x_{1} = 1$$

                                               ___________________     /             ___________________                               \
                                              /              ____      |            /              ____                                |
                                             /   4039   19*\/ 33       |    ___    /   4039   19*\/ 33                                 |
                                          3 /   ----- + ---------      |  \/ 3 *3 /   ----- + ---------                   ___          |
       1                31                \/    15606      5202        |        \/    15606      5202                31*\/ 3           |
x2 = - - - ---------------------------- - ------------------------ + I*|- ------------------------------ + ----------------------------|
       3            ___________________              2                 |                2                           ___________________|
                   /              ____                                 |                                           /              ____ |
                  /   4039   19*\/ 33                                  |                                          /   4039   19*\/ 33  |
           153*3 /   ----- + ---------                                 |                                   153*3 /   ----- + --------- |
               \/    15606      5202                                   \                                       \/    15606      5202   /

$$x_{2} = - \frac{1}{3} - \frac{\sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} - \frac{31}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} + \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}\right)$$

                                               ___________________     /           ___________________                               \
                                              /              ____      |          /              ____                                |
                                             /   4039   19*\/ 33       |  ___    /   4039   19*\/ 33                                 |
                                          3 /   ----- + ---------      |\/ 3 *3 /   ----- + ---------                   ___          |
       1                31                \/    15606      5202        |      \/    15606      5202                31*\/ 3           |
x3 = - - - ---------------------------- - ------------------------ + I*|------------------------------ - ----------------------------|
       3            ___________________              2                 |              2                           ___________________|
                   /              ____                                 |                                         /              ____ |
                  /   4039   19*\/ 33                                  |                                        /   4039   19*\/ 33  |
           153*3 /   ----- + ---------                                 |                                 153*3 /   ----- + --------- |
               \/    15606      5202                                   \                                     \/    15606      5202   /

$$x_{3} = - \frac{1}{3} - \frac{\sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} - \frac{31}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + i \left(- \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2}\right)$$

                ___________________                               
               /              ____                                
       1      /   4039   19*\/ 33                  62             
x4 = - - + 3 /   ----- + ---------  + ----------------------------
       3   \/    15606      5202               ___________________
                                              /              ____ 
                                             /   4039   19*\/ 33  
                                      153*3 /   ----- + --------- 
                                          \/    15606      5202

$$x_{4} = - \frac{1}{3} + \frac{62}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}$$

x4 = -1/3 + 62/(153*(19*sqrt(33)/5202 + 4039/15606)^(1/3)) + (19*sqrt(33)/5202 + 4039/15606)^(1/3)

Sum and product of roots [src]

sum

                                              ___________________     /             ___________________                               \                                             ___________________     /           ___________________                               \                                                                
                                             /              ____      |            /              ____                                |                                            /              ____      |          /              ____                                |                                                                
                                            /   4039   19*\/ 33       |    ___    /   4039   19*\/ 33                                 |                                           /   4039   19*\/ 33       |  ___    /   4039   19*\/ 33                                 |              ___________________                               
                                         3 /   ----- + ---------      |  \/ 3 *3 /   ----- + ---------                   ___          |                                        3 /   ----- + ---------      |\/ 3 *3 /   ----- + ---------                   ___          |             /              ____                                
      1                31                \/    15606      5202        |        \/    15606      5202                31*\/ 3           |     1                31                \/    15606      5202        |      \/    15606      5202                31*\/ 3           |     1      /   4039   19*\/ 33                  62             
1 + - - - ---------------------------- - ------------------------ + I*|- ------------------------------ + ----------------------------| + - - - ---------------------------- - ------------------------ + I*|------------------------------ - ----------------------------| + - - + 3 /   ----- + ---------  + ----------------------------
      3            ___________________              2                 |                2                           ___________________|     3            ___________________              2                 |              2                           ___________________|     3   \/    15606      5202               ___________________
                  /              ____                                 |                                           /              ____ |                 /              ____                                 |                                         /              ____ |                                            /              ____ 
                 /   4039   19*\/ 33                                  |                                          /   4039   19*\/ 33  |                /   4039   19*\/ 33                                  |                                        /   4039   19*\/ 33  |                                           /   4039   19*\/ 33  
          153*3 /   ----- + ---------                                 |                                   153*3 /   ----- + --------- |         153*3 /   ----- + ---------                                 |                                 153*3 /   ----- + --------- |                                    153*3 /   ----- + --------- 
              \/    15606      5202                                   \                                       \/    15606      5202   /             \/    15606      5202                                   \                                     \/    15606      5202   /                                        \/    15606      5202

$$\left(- \frac{1}{3} + \frac{62}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}\right) + \left(\left(1 + \left(- \frac{1}{3} - \frac{\sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} - \frac{31}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} + \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}\right)\right)\right) + \left(- \frac{1}{3} - \frac{\sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} - \frac{31}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + i \left(- \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2}\right)\right)\right)$$

  /           ___________________                               \     /             ___________________                               \
  |          /              ____                                |     |            /              ____                                |
  |  ___    /   4039   19*\/ 33                                 |     |    ___    /   4039   19*\/ 33                                 |
  |\/ 3 *3 /   ----- + ---------                   ___          |     |  \/ 3 *3 /   ----- + ---------                   ___          |
  |      \/    15606      5202                31*\/ 3           |     |        \/    15606      5202                31*\/ 3           |
I*|------------------------------ - ----------------------------| + I*|- ------------------------------ + ----------------------------|
  |              2                           ___________________|     |                2                           ___________________|
  |                                         /              ____ |     |                                           /              ____ |
  |                                        /   4039   19*\/ 33  |     |                                          /   4039   19*\/ 33  |
  |                                 153*3 /   ----- + --------- |     |                                   153*3 /   ----- + --------- |
  \                                     \/    15606      5202   /     \                                       \/    15606      5202   /

$$i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} + \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}\right) + i \left(- \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2}\right)$$

product

/                                          ___________________     /             ___________________                               \\ /                                          ___________________     /           ___________________                               \\                                                                
|                                         /              ____      |            /              ____                                || |                                         /              ____      |          /              ____                                ||                                                                
|                                        /   4039   19*\/ 33       |    ___    /   4039   19*\/ 33                                 || |                                        /   4039   19*\/ 33       |  ___    /   4039   19*\/ 33                                 || /           ___________________                               \
|                                     3 /   ----- + ---------      |  \/ 3 *3 /   ----- + ---------                   ___          || |                                     3 /   ----- + ---------      |\/ 3 *3 /   ----- + ---------                   ___          || |          /              ____                                |
|  1                31                \/    15606      5202        |        \/    15606      5202                31*\/ 3           || |  1                31                \/    15606      5202        |      \/    15606      5202                31*\/ 3           || |  1      /   4039   19*\/ 33                  62             |
|- - - ---------------------------- - ------------------------ + I*|- ------------------------------ + ----------------------------||*|- - - ---------------------------- - ------------------------ + I*|------------------------------ - ----------------------------||*|- - + 3 /   ----- + ---------  + ----------------------------|
|  3            ___________________              2                 |                2                           ___________________|| |  3            ___________________              2                 |              2                           ___________________|| |  3   \/    15606      5202               ___________________|
|              /              ____                                 |                                           /              ____ || |              /              ____                                 |                                         /              ____ || |                                         /              ____ |
|             /   4039   19*\/ 33                                  |                                          /   4039   19*\/ 33  || |             /   4039   19*\/ 33                                  |                                        /   4039   19*\/ 33  || |                                        /   4039   19*\/ 33  |
|      153*3 /   ----- + ---------                                 |                                   153*3 /   ----- + --------- || |      153*3 /   ----- + ---------                                 |                                 153*3 /   ----- + --------- || |                                 153*3 /   ----- + --------- |
\          \/    15606      5202                                   \                                       \/    15606      5202   // \          \/    15606      5202                                   \                                     \/    15606      5202   // \                                     \/    15606      5202   /

$$\left(- \frac{1}{3} - \frac{\sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} - \frac{31}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + i \left(- \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2}\right)\right) \left(- \frac{1}{3} - \frac{\sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} - \frac{31}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}{2} + \frac{31 \sqrt{3}}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}}\right)\right) \left(- \frac{1}{3} + \frac{62}{153 \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}} + \sqrt[3]{\frac{19 \sqrt{33}}{5202} + \frac{4039}{15606}}\right)$$

256
---
289

$$\frac{256}{289}$$

256/289

Numerical answer [src]

x1 = 1.0

x2 = -0.970142608992334 - 0.02986446360174*i

x3 = -0.970142608992334 + 0.02986446360174*i

x4 = 0.940285217984668

x4 = 0.940285217984668

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sqrt^4(17x^2-16)=x equation

Numerical solution:

The solution