Question

Find x, so that 2x + 1x?+*+1 and 3r? - 3x + 3 are consecutive terms of an A.P.​

Answer 1

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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,

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

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

$2x + 2x + 2 = 3x - x + 4$

$0 = x - 3x + 2$

$x = 3x + 2 = 0$

$x - 2x - x + 2 = 0$

$x(x - 2) - 1(x - 2) = 0$

$(x - 2)(x - 1) = 0$

$x = 2 \: or \: x = 1$