Question

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

Answer 1

Answer:

$x=1\\x=-1$

Step-by-step explanation:

$9x^{4} -2x^{2} -7=0\\y=x^{2} \\9y^{2} -2y-7=0\\y=\frac{2\pm\sqrt{(-2)^{2} -4*9(-7)} }{2*9} =\frac{2\pm\sqrt{4+252} }{18} =\frac{2\pm\sqrt{256} }{18}$

$\sqrt{256} =16$

$y=\frac{2+16}{18} =\frac{18}{18} =1 \\or \\y=\frac{2-16}{18} =-\frac{14}{18} =-\frac{7}{9}$

$x^{2} = 1 \\or \\x^{2} =-\frac{7}{9}$

$x=\pm 1$

$x^{2} =-\frac{7}{9}$ has no solution since fot all $x$ on the real line, $x^{2} \geq 0$ and $-\frac{7}{9} < 0.$