What are the solutions to the equation x^4-6x^2+12=7 ?

The solutions to the equation x^4-6x^2+12=7 are x=sqrt(5),x=-sqrt(5),x=1,x=-1

Find the zeros of x^4-6x^2+12=7

The zeros of x^4-6x^2+12=7 are x=sqrt(5),x=-sqrt(5),x=1,x=-1

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x^{4} - 6 x^{2} + 12 = 7

x = 5, x = - 5, x = 1, x = - 1

Decimal Notation

x = 2.23606 \dots, x = - 2.23606 \dots, x = 1, x = - 1

Solution steps

x^{4} - 6 x^{2} + 12 = 7

Move

7

to the left side

x^{4} - 6 x^{2} + 5 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} - 6 u + 5 = 0

Solve

u^{2} - 6 u + 5 = 0 : u = 5, u = 1

u = 5, u = 1

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 5 : x = 5, x = - 5

Solve

x^{2} = 1 : x = 1, x = - 1

The solutions are

x = 5, x = - 5, x = 1, x = - 1

z^{5} - 32 i = 0

x^{3} = 512

3 t^{3} - 3 t^{2} + 4 = 0

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

x^{3} + 2 x^{2} - 4 x - 8 = 0

What are the solutions to the equation x^4-6x^2+12=7 ?
The solutions to the equation x^4-6x^2+12=7 are x=sqrt(5),x=-sqrt(5),x=1,x=-1
Find the zeros of x^4-6x^2+12=7
The zeros of x^4-6x^2+12=7 are x=sqrt(5),x=-sqrt(5),x=1,x=-1