Question

Divide 29 into two parts so that the sum of the squares of the parts is 425.

Answer 1

Let one of the number be ‘a’. 

Given, sum of two numbers is 29 and the sum of their squares is 425 

⇒ a² + (29 – a)² = 425 

⇒ a² + 841 + a² – 58a = 425 

⇒ a² – 29a + 416 = 0 

⇒ a² – 16a – 13a + 208= 0 

⇒ a(a – 16) – 13(a – 16) = 0 

⇒ (a – 13)(a – 16) = 0 

⇒ a = 13, 16