Mathematics : asked on nayellisoto15

07.04.2023

One positive integer is 4 less than twice another. The sun of their squares is 653. Find the integers.
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27.01.2022, solved by verified expert

Bhaskar Singh Bora

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Let one of the integer be x.

So other is 4 less than twice of it, i.e., 2x - 4

Now, the sum of their squares is 653.

Thus,

x² + (2x - 4)² = 653

x² + (4x² + 16 - 16x) = 653

5x² - 16x - 637 = 0

5x² - 65x + 49x - 637 = 0

5x(x - 13) + 49(x - 13) = 0

(5x + 49)(x - 13) = 0

Thus, x = -49/5 or x = 13

Since x is a positive integer, thus x = 13

Other integer = 2x - 4 = (2 × 13) - 4 = 22

Therefore,

Smaller : 13

Larger : 22

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