Question

what are the solutions of the equation (9x^4 - 2x^2 - 7 = 0)? use (u) substitution to solve.

(x = pmsqrt{\frac{7}{9}}) and (x = pm 1)

(x = pmsqrt{\frac{7}{9}}) and (x = pm i)

(x = pm isqrt{\frac{7}{9}}) and (x = pm 1)

(x = pm isqrt{\frac{7}{9}}) and (x = pm i)

Explanation:

Substitute to form a quadratic equation

Using the Quadratic Form Equations knowledge point

$$
LATEXBLOCK0
$$

Solve the quadratic equation for u

Using the Quadratic Formula knowledge point

$$
LATEXBLOCK1
$$

Solve for x using back-substitution

Using the Complex Roots knowledge point

$$
LATEXBLOCK2
$$

Answer:

• (A) \(x = \pm\sqrt{\frac{7}{9}}\) and \(x = \pm1\)
• (B) \(x = \pm\sqrt{\frac{7}{9}}\) and \(x = \pm i\)
• (C) \(x = \pm i\sqrt{\frac{7}{9}}\) and \(x = \pm1\)
• (D) \(x = \pm i\sqrt{\frac{7}{9}}\) and \(x = \pm i\) (Correct answer)