Q19 of 39 Page 91

Find the two consecutive numbers whose squares have the sum 85. Find the two number using the quadratic formula.

Let the two numbers be a & a + 1

As, a2 + (a + 1)2 = 85


⇒ a2 + a2 + 2a + 1 = 85


⇒ 2a2 + 2a – 84 = 0


⇒ a2 + a – 42 = 0


⇒ a2 + 7a – 6a – 42 = 0


⇒ a(a + 7) – 6(a + 7) = 0


⇒ (a – 6)(a + 7) = 0


a = 6 or a = – 7


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