Question

Find X so that X+6,X+12 and X+15 are consecutive terms of a geometric progression.

answer

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Answer 1

Hey there!

Answer:

x = - 18

Step-by-step explanation:

When three numbers are in G.P then,

b² = ac

( x + 12)² = (x + 6) (x + 15)

x² + (12)² + 2× x × 12 = x ( x + 15) + 6(x + 15)

x² + 144 + 24x = x² + 15x + 6x + 90

24x  - 15x - 6x = 90 - 144

3x = - 54

x =  - 54  / 3

x = - 18

Answer 2

■Consecutive terms are x + 6 , x + 12 and x + 15.

★Using this formula :-

b² = ac

(x + 12)² = (x + 6) (x + 15)

★Use identity : (a + b)² = a² + b² + 2ab

⇒ x² + (12)² + 2 × x × 12 = x(x + 15) + 6(x + 15)

⇒ x² + 144 + 24x = x² + 15x + 6x + 90

⇒ 24x  - 15x - 6x = 90 - 144

⇒ 3x = - 54

$\tt{\rightarrow x = \dfrac{-54}{3}}$

x = -18

★Now substitute the value of x :-

(-18) + 6 = -12

(-18) + 12 = -6

(-18) + 15 = -3