1.

The sum of the squares of two consecutive positive integers is 545. Find the integers.

Answer»

Let x be one of the positive integers. Then the other integer is x + 1, x∈Z+

Since the sum of the squares of the integers is 545, we get

x2 + (x + 1)2 = 545

or 2x2 + 2x - 544 = 0

or x2 + x - 272 = 0

x2 + 17x - 16x - 272 = 0

or x(x + 17) - 16(x + 17) = 0

or (x - 16) (x + 17) = 0

Here, x = 16 or x = -17 But, x is a positive integer. Therefore, reject x = - 17 and take x = 16. Hence, two consecutive positive integers are 16 and (16 + 1), i.e., 16 and 17.


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