What are the solutions to the equation 3x^4+2x^2=1 ?

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

Find the zeros of 3x^4+2x^2=1

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

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3 x^{4} + 2 x^{2} = 1

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

Solution steps

3 x^{4} + 2 x^{2} = 1

Move

1

to the left side

3 x^{4} + 2 x^{2} - 1 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

3 u^{2} + 2 u - 1 = 0

Solve

3 u^{2} + 2 u - 1 = 0 : u = \frac{1}{3}, u = - 1

u = \frac{1}{3}, u = - 1

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

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

The solutions are

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

x, (x + y)^{5} = 3

\frac{3 ( x + 3 ) ^{3}}{2} = 96

x^{3} + 4 x^{2} + x + 6 = 0

(y^{2})^{2} = y^{2}

x^{3} - 5 x^{2} + 16 x - 80 = 0

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