Question

What are the solutions of the equation 9x4 – 2x2 – 7 = 0? Use u substitution to solve.
x = plus-or-minus StartRoot seven-ninths EndRoot and x = ±1
x = plus-or-minus StartRoot seven-ninths EndRoot and x = ±i
x = plus-or-minus i StartRoot seven-ninths EndRoot and x = ±1
x = plus-or-minus i StartRoot seven-ninths EndRoot and x = ±i

Answer 1

Let u = x^2. Then 9u^2 − 2u − 7 = 0.
Discriminant Δ = (−2)^2 − 4·9·(−7) = 4 + 252 = 256, so u = (2 ± 16)/18 = 1 or −7/9.

Thus x^2 = 1 → x = ±1, and x^2 = −7/9 → x = ± i√(7/9) = ± i√7/3.

So the correct choice is: x = ± i√(7/9) and x = ±1.