What are the solutions to the equation 6x^4-45x^2+81=0 ?

The solutions to the equation 6x^4-45x^2+81=0 are x= 3/(sqrt(2)),x=-3/(sqrt(2)),x=sqrt(3),x=-sqrt(3)

Find the zeros of 6x^4-45x^2+81=0

The zeros of 6x^4-45x^2+81=0 are x= 3/(sqrt(2)),x=-3/(sqrt(2)),x=sqrt(3),x=-sqrt(3)

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6 x^{4} - 45 x^{2} + 81 = 0

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

Solution steps

6 x^{4} - 45 x^{2} + 81 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

6 u^{2} - 45 u + 81 = 0

Solve

6 u^{2} - 45 u + 81 = 0 : u = \frac{9}{2}, u = 3

u = \frac{9}{2}, u = 3

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

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

The solutions are

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

x^{8} + 16 = 17 x^{4}

y^{3} + 5 y^{2} - 36 y - 180 = 0

x^{4} + 49 x^{2} = 0

(x - 1) (x + 2)^{2} (x^{2} - 6 x + 10) = 0

3 y (3 y - 5) (2 y + 7) = 0

What are the solutions to the equation 6x^4-45x^2+81=0 ?
The solutions to the equation 6x^4-45x^2+81=0 are x= 3/(sqrt(2)),x=-3/(sqrt(2)),x=sqrt(3),x=-sqrt(3)
Find the zeros of 6x^4-45x^2+81=0
The zeros of 6x^4-45x^2+81=0 are x= 3/(sqrt(2)),x=-3/(sqrt(2)),x=sqrt(3),x=-sqrt(3)