Question

Divide 57 into two parts whose product is 680. 

Answer 1

Let the two parts be x and (57 – x). 

According to the given condition, 

x(57 – x) = 680 

⇒ 57x – x² = 680 

⇒ x² – 57x + 680 = 0 

⇒ x² – 40x – 17x + 680 = 0

⇒ x(x – 40) – 17(x – 40) = 0 

⇒ (x – 40) (x – 17) = 0 

⇒ x – 40 = 0 or x – 17 = 0 

⇒ x = 40 or x = 17 

When x = 40, 

57 – x = 57 – 40

= 17 

When x = 17, 

57 – x = 57 – 17

= 40 

Hence, the required parts are 17 and 40.