Question

if x+9,x-6,4 are first three elements of GP then c 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

$\huge\underline\mathfrak\purple{Answer}$

If the number are in gp,

Then,

(x-6)²=4(x+9)

x²-12x+36=4x+36

x²-16x=0

x=0 or x=16.

So the numbers are,

25 ,10 and 4

Thanks! ❤