Question

find the value of of x if 2x+1,x^2+x+1,3x^2+-3x+3​

Answer 1

Step-by-step explanation:

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.

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