Question

Find x so that 2x+1, x2+x+1, 3x2-3x+3 are three consecutive terms of an



a.P

Answer 1

As the terms are in ap, therefore common difference between the given consecutive terms will be equal.

So,

(x2 + x + 1) - (2x + 1) = (3x2- 3x+ 3) - (x2 + x + 1)

⇒ 2(x2 + x + 1) = (3x2- 3x+ 3) + (2x + 1)

⇒ 2x2 + 2x + 2 = 3x2- x + 4

⇒ 0 = x2 - 3x + 2

⇒ x2 - 3x + 2 = 0

⇒ x2 - 2x - x + 2 = 0

⇒ x(x - 2) -1(x - 2) = 0

⇒ (x - 2)(x -1) = 0

⇒ x = 2 or x = 1

Here, x = 1 can't be possible because on putting x = 1 we are not getting the given terms in a.p.

Answer 2

Answer:

Refer to the above attachment bro.....