What are the solutions to the equation w^4-18w^2+81=0 ?

The solutions to the equation w^4-18w^2+81=0 are w=3,w=-3

Find the zeros of w^4-18w^2+81=0

The zeros of w^4-18w^2+81=0 are w=3,w=-3

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w^{4} - 18 w^{2} + 81 = 0

w = 3, w = - 3

Solution steps

w^{4} - 18 w^{2} + 81 = 0

Rewrite the equation with

u = w^{2}

and

u^{2} = w^{4}

u^{2} - 18 u + 81 = 0

Solve

u^{2} - 18 u + 81 = 0 : u = 9

u = 9

Substitute back

u = w^{2},

solve for

w

Solve

w^{2} = 9 : w = 3, w = - 3

The solutions are

w = 3, w = - 3

9 x^{4} - 24 x^{3} + 16 x^{2} = 0

x^{6} - 26 x^{3} - 27 = 0

x^{3} - 5 x^{2} + 2 x + 8 = 0

x^{4} - 2 x^{2} = 2 x^{2}

4 (x^{4} + 1) = 5 x^{2}

What are the solutions to the equation w^4-18w^2+81=0 ?
The solutions to the equation w^4-18w^2+81=0 are w=3,w=-3
Find the zeros of w^4-18w^2+81=0
The zeros of w^4-18w^2+81=0 are w=3,w=-3