For what values of x, the numbers (x + 9), (x - 6) and 4 are in G.P?

Question

KnowledgeBoat · Accepted Answer

We know that,

In G.P. we have constant common ratio.

$\dfrac{x - 6}{x + 9} = \dfrac{4}{x - 6}$

Solving,

⇒ (x - 6)² = 4(x + 9)

⇒ x² - 12x + 36 = 4x + 36

⇒ x² - 12x + 36 - 4x - 36 = 0

⇒ x² - 16x = 0

⇒ x(x - 16) = 0

⇒ x = 0 or (x - 16) = 0

⇒ x = 0 or x = 16.

Hence, x = 0 or x = 16.

Mathematics