Question

Find Three consecutive integers such that the square of the second increased by the third is 43

Answer 1

They are 3 consecutive integers. Let the first one be X, the second will be X + 1 and the third will be X + 2.

Now, according to the problem statement, the square of the second is (X+1)^2. Increasing this by the third means :
\[(x+1)^2+(x+2) \] where (X + 2) is the third number.

So, the equation is :
\[(x+1)^2 + (x+2) = 43\]

Solve it for x, and you can get the three consecutive integers.