Question

What are the solutions of the equation 9x^4 – 2x^2 – 7 = 0? Use u substitution to solve.

Answer 1

$9x^4 - 2x^2 - 7 = 0 \\ \text{substitution: } x^2=t, \ \ t\ \textgreater \ 0\\ 9t^2-2t-7\ \textgreater \ 0 \\ D=b^2-4ac=(-2)^2-4*9*(-7)=4+252 = 256 \\ t_{1,2}= \frac{-bб \sqrt{D} }{2a}= \frac{2б 16 }{18} \\ t_1=- \frac{14}{18} \ \ \ \ \O \\ \boxed{t_2=1} \\ \\x^2=1\\x=б \sqrt{1} \\ x=б1$

Answer: x=-1, x=1