Question

find x so that 2x+1, x^2+x+1 and 3x^2-3x+3 are consecutive terms of an arithmetic progression

Answer 1

As they are consecutive

2x+1+3x^2-3x+3.

_____________. =. X^2+x+1

2

3x^2-x+4

_______. =X^2+x+1

2

3x^2-x+4. = 2x^2+2x+2

X^2-3x+2=0

Then solve using splitting the middle term

And the answer= 1 or 2