Find two consecutive natural numbers, the sum of whose squares is 145. (CBSE 2012)
Let us suppose that two consecutive numbers are x and x + 1.
According to the given condition,
x2 + (x + 1)2= 145
x2 + x2+ 2x + 1 = 145
2x2 + 2x + 1 = 145
2x2 + 2x - 144 = 0
x2 + x - 72 = 0
x2 + 9x - 8x - 72 = 0
x(x + 9) - 8(x + 9) = 0
(x + 9) (x - 8) = 0
x = -9, 8
Accepting only positive number, we get
Two number would be x = 8 and x + 1 = 9
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