Divide 20 into two parts such that the sum of the square of the parts is 218.

Question

Philoid · Accepted Answer

Let the divided two parts be x and 20 – x.

⇒ x² + (20 – x)² = 218

⇒ x² + 400 – 40x + x² = 218

⇒ 2x² – 40x + 182 = 0

Dividing the whole equation by 2, we get –

⇒ x² – 20x + 91 = 0

⇒ x² – (7 + 13)x + 91 = 0

⇒ x² – 7x – 13x + 91 = 0

⇒ x(x – 7) – 13(x – 7) = 0

⇒ (x – 7)(x – 13) = 0

⇒ x – 7 = 0 or x – 13 = 0

⇒ x = 7 or x = 13

∴ the two parts are 7 and 13.