Question

if×-2,x,x+3 are first three elements of gp then x is​

Answer 1

Answer:

Step-by-step explanation:

x square = (x-2)(x+3)

               = x sq + 3x -2x -6

              = x sq +x - 6

              = x sq  + 3x -2x -6

              = x(x+3) - 2 (x+3)

              = (x+3) ( x-2)

               x = 2, -3

Answer 2

Concept : If in a series, The next term is obtained by multiplying ( or dividing) the earlier term by a constant number. Then, Such Series is known as Geometrical progression.

Formula : If a, b, c are the consecutive term of G. P, then b² = ac

(or)

a, b, c are consecutive terms of AP if and only if b² = ac.

Given, x - 2, x, x + 3 are the first three elements of G. P.

As discussed above,

⇒ (x)² = (x-2)(x+3)

⇒x² = x² - 2x + 3x - 6

⇒ 0 = x - 6

⇒x = 6

Therefore, Value of x for which x - 2, x, x + 3 can be in a G. P is x = 6