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Question
Find two consecutive positive odd numbers, the sum of whose squares is 74.
Solution
Let the consecutive positive odd numbers be x and x + 2.
From the given information,
x2 + (x + 2)2 = 74
2x2 + 4x + 4 = 74
2x2 + 4x – 70 = 0
x2 + 2x – 35 = 0
(x + 7)(x – 5) = 0
x = –7, 5
Since, the numbers are positive, so, x = 5.
Thus, the numbers are 5 and 7.
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