Question

Find two negative consecutive integers such that the square of the first is five more than the second. Find the integers.

Answer 1

the two consecutive negative integers are -2 and -1.

Explanation:

Represent these negative integers by m and n.

Then (because the integers are consecutive) n = m + 1, and m^2 = n + 5.

Substituting m + 1 for n in the second equation, we get:

m^2 = m + 1 + 5, or

m^2 - m - 6 = 0

This factors into (m - 3)(m + 2) = 0. The only negative root is -2.

Thus, the two consecutive negative integers are -2 and -1.

Check: Is the square of the first five more than the second?

Is (-2)^2 = -1 + 5? YES

The integers aer -2 and -1.