Question

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

Answer 1

`x=1\\x=-1`

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} =(2\pm√(4+252) )/(18) =(2\pm√(256) )/(18)`

`√(256) =16`

`y=(2+16)/(18) =(18)/(18) =1 \\or \\y=(2-16)/(18) =-(14)/(18) =-(7)/(9)`

`x^(2) = 1 \\or \\x^(2) =-(7)/(9)`

`x=\pm 1`

`x^(2) =-(7)/(9)` has no solution since fot all
`x` on the real line,
`x^(2) \geq 0` and
`-(7)/(9) < 0.`