Solve for x: 9x² - 6px + (p² - q²) = 0

Question

Solve for x: 9x² - 6px + (p² - q²) = 0

Answer 1

Given equation

9x² - 6px + (p² - q²) = 0

Comparing equation with ax² + bx + c = 0

a = 9, b = -6p, c = (p² - q²)

We know that

D = b² - 4ac

Putting values

Now, 

Using quadratic formula to find roots

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

Putting the values

Answer 2

Given equation is 9x² – 6px + (p² – q²) = 0.

a = 9, b = − 6p, c = p² − q²

D = b² − 4ac

= (− 6p)² − 4(9)(p² − q²)

= 36q²

\(x = \frac{-b\pm \sqrt D}{2q} \)

\(= \frac{6p \pm 6q}{18}\)

\(= \frac{p \pm q}3\)

\(= \frac{p + q}3\) or \( \frac{p - q}3\)