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The squares of two consecutive positive integers total is 145 What are the numbers?
Wiki User
∙ 15y ago
Let the first integer be x, and the second one be x + 1, then we have:
x^2 + (x + 1)^2 = 145
x^2 + x^2 + 2x + 1 = 145
2x^2 + 2x + 1 = 145
2x^2 + 2x + 1 - 145 = 145 - 145
2x^2 + 2x - 144 = 0 divide by 2 to both sides
x^2 + x - 72 = 0
(x - 8)(x + 9) = 0
x = 8 or x = -9 ignore x = -9 since the numbers are positive
x + 1 = 8 + 1 = 9
Thus, the consecutive positive integers are 8 and 9.
Check:
8^2 + 9^2 = 135 ?
64 + 81 = 145 ?
145 = 145 True
Wiki User
∙ 15y ago
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