What are the solutions to the equation 7x^4-6x^2-1=0 ?

The solutions to the equation 7x^4-6x^2-1=0 are x=1,x=-1,x= 1/(sqrt(7))i,x=-1/(sqrt(7))i

Find the zeros of 7x^4-6x^2-1=0

The zeros of 7x^4-6x^2-1=0 are x=1,x=-1,x= 1/(sqrt(7))i,x=-1/(sqrt(7))i

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7 x^{4} - 6 x^{2} - 1 = 0

x = 1, x = - 1, x = \frac{1}{7} i, x = - \frac{1}{7} i

Solution steps

7 x^{4} - 6 x^{2} - 1 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

7 u^{2} - 6 u - 1 = 0

Solve

7 u^{2} - 6 u - 1 = 0 : u = 1, u = - \frac{1}{7}

u = 1, u = - \frac{1}{7}

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

x^{2} = - \frac{1}{7} : x = \frac{1}{7} i, x = - \frac{1}{7} i

The solutions are

x = 1, x = - 1, x = \frac{1}{7} i, x = - \frac{1}{7} i

x^{5} - x^{4} - 3 x^{3} = 0

x^{4} (x^{3} - 9) = - 8 x

6 + x^{3} = 222

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

2 x^{3} + 5 x - 1 = 0

What are the solutions to the equation 7x^4-6x^2-1=0 ?
The solutions to the equation 7x^4-6x^2-1=0 are x=1,x=-1,x= 1/(sqrt(7))i,x=-1/(sqrt(7))i
Find the zeros of 7x^4-6x^2-1=0
The zeros of 7x^4-6x^2-1=0 are x=1,x=-1,x= 1/(sqrt(7))i,x=-1/(sqrt(7))i