Question

There are two consecutive odd integers. The

square of the smaller one is one hundred
fifty-four more than the larger one. What
are the two integers?

Answer 1

13, 15

Explanation:

Let x represent the smaller of the two integers. Then the larger is x+2. The required relation is ...

x² = 154 +(x +2) . . . . . . the smaller squared is 154 more than the larger

x² -x = 156 . . . . . . . . . . subtract x

x² -x +1/4 = 156.25 . . . complete the square

(x -1/2) = √156.25 = 12.5 . . . . take the square root

x = 13 . . . . . add 1/2

The two integers are 13 and 15.

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Check

13² -15 = 169 -15 = 154 . . . as required