Question

15x^4 - 11x^2 + 2 = 0

Answer 1

Quadratic in form. Let x^2=u. Substitute to get a quadratic equation in u. Solve this equation. Substitute x^2 in for the solutions and solve for x. Check your answers to make sure they meet the specifications of the problem.

Answer 2

\[15x^4 - 11x^2 + 2 = 0\]\[15(x^2)^2 - 11x^2 +2 =0\]\[(3x^2 -1)(5x^2-2)=0\]\[3x^2 -1=0 \ or\ 5x^2-2=0\]
x^2 = 1/3 or x^2 = 2/5
\[x = \pm \sqrt{1/3}\] or \[x= \pm \sqrt{2/5}\]

Answer 3

That's what I thought it was Calliisto, needed a confirmation. Thank you.

Answer 4

Welcome :)

Answer 5

\[15x^4 - 11x^2 + 2 = 0\implies 15u^2-11u+2=0\implies 15u^2-6u-5u+2=0\]\[\implies 3u(5u-2)-(5u-2)=(3u-1)(5u-2)=0\implies u=\frac{1}{3}~or~u=\frac{2}{5}\]\[\implies x^2=\frac{1}{3}~or~x^2=\frac{2}{5}\implies x=\pm \frac{\sqrt3}{3}~or~x=\pm \frac{\sqrt{10}}{5}\]