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The sum of the squares of two consecutive natural numbers is 145. Find those numbers. A. 6,7B. 10,11C. 8,9D. 10,9

Solution

x²+ (x + 1)² = 145
⇒2x ²+ 2x + 1 = 145
⇒2x ² + 2x – 144 = 0
⇒x ² + x – 72 = 0
⇒x(x + 9) – 8(x + 9) = 0
⇒x = -9,8

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