What are the solutions to the equation w^4+36=13w^2 ?

The solutions to the equation w^4+36=13w^2 are w=3,w=-3,w=2,w=-2

Find the zeros of w^4+36=13w^2

The zeros of w^4+36=13w^2 are w=3,w=-3,w=2,w=-2

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w^{4} + 36 = 13 w^{2}

w = 3, w = - 3, w = 2, w = - 2

Solution steps

w^{4} + 36 = 13 w^{2}

Move

13 w^{2}

to the left side

w^{4} + 36 - 13 w^{2} = 0

Write in the standard form

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

w^{4} - 13 w^{2} + 36 = 0

Rewrite the equation with

u = w^{2}

and

u^{2} = w^{4}

u^{2} - 13 u + 36 = 0

Solve

u^{2} - 13 u + 36 = 0 : u = 9, u = 4

u = 9, u = 4

Substitute back

u = w^{2},

solve for

w

Solve

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

Solve

w^{2} = 4 : w = 2, w = - 2

The solutions are

w = 3, w = - 3, w = 2, w = - 2

2 x^{3} - 8 x + 15 x = 18

x^{5} - 3 x^{2} + 4

x^{3} - 9 x^{2} + 8 x + 60 = 0

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

4 x^{3} - 4 x + 3 = 0

What are the solutions to the equation w^4+36=13w^2 ?
The solutions to the equation w^4+36=13w^2 are w=3,w=-3,w=2,w=-2
Find the zeros of w^4+36=13w^2
The zeros of w^4+36=13w^2 are w=3,w=-3,w=2,w=-2