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12. Thesum of squares of two consecutive naturalnumbers is 421. Find the numbers.

Answer»

Let the two consecutive natural numbers be x and (x + 1)

Given x2+ (x + 1)2= 421x2+ x2+ 2x + 1 – 421 = 02x2+ 2x – 420 = 0x2+ x – 210 = 0x2+ 15x – 14x – 210 = 0(x + 15)(x – 14) = 0Hence x = -15 or 14Since x is a natural numberThus x = 14x + 1 = 15Therefore the two consecutive numbers are 14 and 15.



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