if (x+9), (x+6), 4 are in geometric progession, then the value of X is. Created by shubhamtiwari3016201. Math

if (x+9), (x+6), 4 are in geometric progession, then the value of X is...

Correct Question :–

▪︎ if (x + 9), (x - 6), 4 are in geometric progession, then the value of X is –

(a) 1 (b) 2 (c) -3 (d) 0

ANSWER :–

$\\ \longrightarrow \: \: { \red { \bold{ x = 0 \: \: , \: \: x = 16}}} \\$

EXPLANATION :–

GIVEN :–

• Three terms (x + 9) , (x + 6) , 4 are in Geometrical progression (G.P.)

TO FIND :–

• The value of 'x'.

SOLUTION :–

• We know that If three terms a , b and c are in G.P. , then –

$\\ \implies \large{ \green{ \boxed{ \bold{ {b}^{2} = a.c }}}} \\$

• So that –

$\\ \implies { \bold{ {(x - 6)}^{2} = (x + 9) \times 4 }} \\$

$\\ \implies { \bold{ {x}^{2} - 12x + 36= 4x + 36 \: \: \: \: \: \: [ \: \because \: {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab ]}} \\$

$\\ \implies { \bold{ {x}^{2} - 12x - 4x + \cancel{36}= \cancel{ 36} }} \\$

$\\ \implies { \bold{ {x}^{2} - 16x = 0 }} \\$

$\\ \implies { \bold{ x(x - 16) = 0 }} \\$

$\\ \implies { \bold{ x = 0 \: \: , \: \: x = 16}} \\$

• Both are satisfying the condition of G.P. , But according to the Options , option (d) is correct.

Answer:

x+9,x−6,4 are three consecutive terms of a G.P.

⇒ (x-6)/(x+9) = (4)/(x-6)

⇒(x−6)²=4x+36

⇒x²−12x+36=4x+36

⇒x²−16x=0

⇒x(x−16)=0

∴x=0,16

Hence the answer is 0

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