What are the solutions to the equation solvefor y,x^4+y^4=x^2y^2 ?

The solutions to the equation solvefor y,x^4+y^4=x^2y^2 are

Find the zeros of solvefor y,x^4+y^4=x^2y^2

The zeros of solvefor y,x^4+y^4=x^2y^2 are

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solve for

y, x^{4} + y^{4} = x^{2} y^{2}

y = \frac{3 x}{2} + \frac{x}{2} i, y = - \frac{3 x}{2} - \frac{x}{2} i, y = - \frac{x ^{2}}{4} + \frac{3 x ^{2}}{4 - \frac{x ^{2}}{4}} i, y = - - \frac{x ^{2}}{4} - \frac{3 x ^{2}}{4 - \frac{x ^{2}}{4}} i, y = \frac{3 x}{2} - \frac{x}{2} i, y = - \frac{3 x}{2} + \frac{x}{2} i, y = - \frac{x ^{2}}{4} - \frac{3 x ^{2}}{4 - \frac{x ^{2}}{4}} i, y = - - \frac{x ^{2}}{4} + \frac{3 x ^{2}}{4 - \frac{x ^{2}}{4}} i

Solution steps

x^{4} + y^{4} = x^{2} y^{2}

Move

x^{2} y^{2}

to the left side

x^{4} + y^{4} - x^{2} y^{2} = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + x = 0

y^{4} - x^{2} y^{2} + x^{4} = 0

Rewrite the equation with

u = y^{2}

and

u^{2} = y^{4}

u^{2} - x^{2} u + x^{4} = 0

Solve

u^{2} - x^{2} u + x^{4} = 0 : u = \frac{x ^{2}}{2} + i \frac{3 x ^{2}}{2}, u = \frac{x ^{2}}{2} - i \frac{3 x ^{2}}{2}

u = \frac{x ^{2}}{2} + i \frac{3 x ^{2}}{2}, u = \frac{x ^{2}}{2} - i \frac{3 x ^{2}}{2}

Substitute back

u = y^{2},

solve for

y

Solve

y^{2} = \frac{x ^{2}}{2} + i \frac{3 x ^{2}}{2} : y = \frac{3 x}{2} + \frac{x}{2} i, y = - \frac{3 x}{2} - \frac{x}{2} i, y = - \frac{x ^{2}}{4} + \frac{3 x ^{2}}{4 - \frac{x ^{2}}{4}} i, y = - - \frac{x ^{2}}{4} - \frac{3 x ^{2}}{4 - \frac{x ^{2}}{4}} i

Solve

y^{2} = \frac{x ^{2}}{2} - i \frac{3 x ^{2}}{2} : y = \frac{3 x}{2} - \frac{x}{2} i, y = - \frac{3 x}{2} + \frac{x}{2} i, y = - \frac{x ^{2}}{4} - \frac{3 x ^{2}}{4 - \frac{x ^{2}}{4}} i, y = - - \frac{x ^{2}}{4} + \frac{3 x ^{2}}{4 - \frac{x ^{2}}{4}} i

The solutions are

y = \frac{3 x}{2} + \frac{x}{2} i, y = - \frac{3 x}{2} - \frac{x}{2} i, y = - \frac{x ^{2}}{4} + \frac{3 x ^{2}}{4 - \frac{x ^{2}}{4}} i, y = - - \frac{x ^{2}}{4} - \frac{3 x ^{2}}{4 - \frac{x ^{2}}{4}} i, y = \frac{3 x}{2} - \frac{x}{2} i, y = - \frac{3 x}{2} + \frac{x}{2} i, y = - \frac{x ^{2}}{4} - \frac{3 x ^{2}}{4 - \frac{x ^{2}}{4}} i, y = - - \frac{x ^{2}}{4} + \frac{3 x ^{2}}{4 - \frac{x ^{2}}{4}} i

x^{3} + 6 x^{2} + 8 x + 10

2 x^{3} - 6 x^{2} - 3 x - 10 = 0

z^{3} - 8 i = 0

3 x^{3} + 7 x^{2} + 6 x - 8 = 0

x^{4} + 55 x^{2} - 576

What are the solutions to the equation solvefor y,x^4+y^4=x^2y^2 ?
The solutions to the equation solvefor y,x^4+y^4=x^2y^2 are
Find the zeros of solvefor y,x^4+y^4=x^2y^2
The zeros of solvefor y,x^4+y^4=x^2y^2 are