What are the solutions to the equation 72x^4-x^2-1=0 ?

The solutions to the equation 72x^4-x^2-1=0 are x= 1/(2sqrt(2)),x=-1/(2sqrt(2)),x= 1/3 i,x=-1/3 i

Find the zeros of 72x^4-x^2-1=0

The zeros of 72x^4-x^2-1=0 are x= 1/(2sqrt(2)),x=-1/(2sqrt(2)),x= 1/3 i,x=-1/3 i

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72 x^{4} - x^{2} - 1 = 0

x = \frac{1}{2 2}, x = - \frac{1}{2 2}, x = \frac{1}{3} i, x = - \frac{1}{3} i

Solution steps

72 x^{4} - x^{2} - 1 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

72 u^{2} - u - 1 = 0

Solve

72 u^{2} - u - 1 = 0 : u = \frac{1}{8}, u = - \frac{1}{9}

u = \frac{1}{8}, u = - \frac{1}{9}

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = \frac{1}{8} : x = \frac{1}{2 2}, x = - \frac{1}{2 2}

Solve

x^{2} = - \frac{1}{9} : x = \frac{1}{3} i, x = - \frac{1}{3} i

The solutions are

x = \frac{1}{2 2}, x = - \frac{1}{2 2}, x = \frac{1}{3} i, x = - \frac{1}{3} i

(1 + x)^{5} = 1.24

6 x^{9} - 72 x^{7} - 7 x^{2} + 96 x - 63 = 0

- x^{3} - 13 x^{2} - 12 x + 10 = 0

x^{4} + 10 x^{2} - 11 = 0

12 x^{3} + 12 x^{2} - 24 x - 24 = 0

What are the solutions to the equation 72x^4-x^2-1=0 ?
The solutions to the equation 72x^4-x^2-1=0 are x= 1/(2sqrt(2)),x=-1/(2sqrt(2)),x= 1/3 i,x=-1/3 i
Find the zeros of 72x^4-x^2-1=0
The zeros of 72x^4-x^2-1=0 are x= 1/(2sqrt(2)),x=-1/(2sqrt(2)),x= 1/3 i,x=-1/3 i