Question

Two.Consecutive even positive integer sum of whose.Squares is 1060

Answer 1

• Let two positive integers be M and M + 2.

» Sum of square of two even positive integers is 1060.

⇒ (M)² + (M + 2)² = 1060

⇒ M² + M² + 4 + 4M = 1060

⇒ 2M² + 4M = 1060 - 4

⇒ 2M² + 4M = 1056

⇒ 2M² + 4M - 1056 = 0

Take 2 common

⇒ 2(M² + 2M - 528) = 0

⇒ M² + 2M - 528 = 0

⇒ M² + 24M - 22M - 528 = 0

⇒ M (M + 24) - 22 (M + 24) = 0

⇒ (M - 22) (M + 24) = 0

• M - 22 = 0

⇒ M = 22

• M + 24 = 0

⇒ M = - 24 (neglected)

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One positive even integer is 22 (M) and other is 24 (M + 2)

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