1.

Find two consecutive numbers whose squares have the sum of 85

Answer»

Let the consecutive numbers be ‘a’ and a + 1. 

Given, sum of squares is 85 

⇒ a2 + (a+ 1)2 = 85 

⇒ a2 + a2 + 2a + 1 = 85 

⇒ a2 + a – 42 = 0 

⇒ a2 + 7a – 6a – 42 = 0 

⇒ a(a + 7) – 6(a + 7) = 0 

⇒ (a – 6)(a + 7) = 0 

⇒ a = 6, -7 

Numbers are, 6, 7 or -7, -6



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