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Popular >

solvefor y,x^3+4xy^2-27=y^4

Solution

solve for

y, x^{3} + 4 x y^{2} - 27 = y^{4}

Solution

y = 2 x + x^{3} + 4 x^{2} - 27, y = - 2 x + x^{3} + 4 x^{2} - 27, y = 2 x - x^{3} + 4 x^{2} - 27, y = - 2 x - x^{3} + 4 x^{2} - 27

Solution steps

x^{3} + 4 x y^{2} - 27 = y^{4}

Switch sides

y^{4} = x^{3} + 4 x y^{2} - 27

Move

27

to the left side

y^{4} + 27 = x^{3} + 4 x y^{2}

Move

4 x y^{2}

to the left side

y^{4} + 27 - 4 x y^{2} = x^{3}

Move

x^{3}

to the left side

y^{4} + 27 - 4 x y^{2} - x^{3} = 0

Write in the standard form

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

y^{4} - 4 x y^{2} + 27 - x^{3} = 0

Rewrite the equation with

u = y^{2}

and

u^{2} = y^{4}

u^{2} - 4 xu + 27 - x^{3} = 0

Solve

u^{2} - 4 xu + 27 - x^{3} = 0 : u = 2 x + x^{3} + 4 x^{2} - 27, u = 2 x - x^{3} + 4 x^{2} - 27

u = 2 x + x^{3} + 4 x^{2} - 27, u = 2 x - x^{3} + 4 x^{2} - 27

Substitute back

u = y^{2},

solve for

y

Solve

y^{2} = 2 x + x^{3} + 4 x^{2} - 27 : y = 2 x + x^{3} + 4 x^{2} - 27, y = - 2 x + x^{3} + 4 x^{2} - 27

Solve

y^{2} = 2 x - x^{3} + 4 x^{2} - 27 : y = 2 x - x^{3} + 4 x^{2} - 27, y = - 2 x - x^{3} + 4 x^{2} - 27

The solutions are

y = 2 x + x^{3} + 4 x^{2} - 27, y = - 2 x + x^{3} + 4 x^{2} - 27, y = 2 x - x^{3} + 4 x^{2} - 27, y = - 2 x - x^{3} + 4 x^{2} - 27

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