Find two consecutive numbers whose squares have the sum of 85
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