What are the solutions to the equation (x^2-5)^2-3(x^2-5)=4 ?

The solutions to the equation (x^2-5)^2-3(x^2-5)=4 are x=3,x=-3,x=2,x=-2

Find the zeros of (x^2-5)^2-3(x^2-5)=4

The zeros of (x^2-5)^2-3(x^2-5)=4 are x=3,x=-3,x=2,x=-2

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(x^{2} - 5)^{2} - 3 (x^{2} - 5) = 4

x = 3, x = - 3, x = 2, x = - 2

Solution steps

(x^{2} - 5)^{2} - 3 (x^{2} - 5) = 4

Expand

(x^{2} - 5)^{2} - 3 (x^{2} - 5) : x^{4} - 13 x^{2} + 40

x^{4} - 13 x^{2} + 40 = 4

Move

4

to the left side

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

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{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 = x^{2},

solve for

x

Solve

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

Solve

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

The solutions are

x = 3, x = - 3, x = 2, x = - 2

x^{4} - x^{3} - 1 = 0

m^{3} = \frac{8}{27}

3 x^{4} - 3 x = 0

25 x^{4} + 4 = 29 x^{2}

8 x^{3} + 3 x^{2} - 16 x - 1 = 0

What are the solutions to the equation (x^2-5)^2-3(x^2-5)=4 ?
The solutions to the equation (x^2-5)^2-3(x^2-5)=4 are x=3,x=-3,x=2,x=-2
Find the zeros of (x^2-5)^2-3(x^2-5)=4
The zeros of (x^2-5)^2-3(x^2-5)=4 are x=3,x=-3,x=2,x=-2