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

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