Question

If x + 9, X-6, 4 are first three elements of
GP then x is
​

Answer 1

Answer:

The values of x are 0 and 16.

Solution:

We know that if a, b, c are in GP, then

b/a = c/b ,

where b/a and c/b are called common ratios.

The given GP is x + 9, x - 6, 4

Using the above definition, we get

(x - 6)/(x + 9) = 4/(x - 6)

or, (x - 6) (x - 6) = 4 (x + 9)

or, x² - 12x + 36 = 4x + 36

or, x² - 16x = 0

or, x (x - 16) = 0

Either x = 0 or, x - 16 = 0

i.e., x = 0, 16

Therefore, the values of x are 0, 16.

Further we can find the GP as

9, - 6, 4 (when x = 0) and

25, 10, 4 (when x = 16)

Answer 2

The value of x is 0 or 16.

Explanation:

The first three elements of  GP are:

x + 9, x - 6 and  4

To find, the value of x = ?

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

⇒ $\dfrac{x-6}{x+9}=\dfrac{4}{x-6}$

⇒ $(x-6)(x-6)=4(x+9)$

⇒ $(x-6)^2=4x+36$

⇒ $x^{2}-12x+36=4x+36$

⇒ $x^{2}-12x-4x=0$

⇒ $x^{2}-16x=0$

⇒ $x(x-16)=0$

∴ x = 0 or 16

Hence, the value of x is 0 or 16.