Answered

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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?

Sagot :

sqdancefan

Answer:

  13, 15

Step-by-step 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.

__

Check

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

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