1.

Find two consecutive positive odd numbers, the sum of whose squares if 74.

Answer»

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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