Question

find x, so that 3x+1, x^2-2x+1 and 2x^2-6x+2 are consecutive terms of an ap.(plz with full method)​

Answer 1

Step-by-step explanation:

Given, 2x+1, x^2 +x+1 and 3x^2 - 3x+ 3 are the consecutive terms of an A.P.

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

So,

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

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

⇒ 2x + 2x + 2 = 3x - x + 4

⇒ 0 = x - 3x + 2

⇒ x - 3x + 2 = 0

⇒ x - 2x - x + 2 = 0

⇒ x(x - 2) -1(x - 2) = 0

⇒ (x - 2)(x -1) = 0

⇒ x = 2 or x = 1