Question

it x+9,x-6,4 are first three elements of go them x is​

Answer 1

For what value of x, the numbers (x+9),(x-6) and 4 are in g.p

Let these be in g.p so that,

(x-6)^2=4(x+9)

x2-12x+36=4x+36

x^2-16x=0

x=0 or x=16.

Therefore, when x=16, the numbers in g.p are

25,10 and 4.

where the common ratio is 2.5

Answer 2

The first three elements of G.P. are "(9, - 6, 4) or (25, 10, 4)".

Step-by-step explanation:

The given first three elements of G.P.

x + 9, x - 6, 4

∴ Common ratio(r) $\dfrac{Second term}{First term} = \dfrac{Third term}{Second term}$

⇒$\dfrac{x-6}{x+9}= \dfrac{4}{x-6}$

⇒ $(x-6)^{2} =4(x+9)$

⇒  $x^{2}-12x+36=4x+36$

⇒  $x^{2}-12x-4x=0$

⇒ $x^{2}-16x=0$

∴$x(x-16)=0$

∴ x = 0 or 16

Put x = 0,

The first three elements of G.P.

0 + 9, 0 - 6, 4 = 9, - 6, 4

Put x = 16,

The first three elements of G.P.

16 + 9, 16 - 6, 4 = 25, 10, 4

Hence, the first three elements of G.P. are (9, - 6, 4) or (25, 10, 4).