The sum of two positive numbers is 20% of the sum of their squares and 25% of the difference of their squares. If the numbers are x and y the,

Explanation

20 Given x+y = 100 × (x2 + y2 ) 1 ⇒ x+y = 5 × (x2 + y2 ) ⇒ x2 + y2 = 5(x+y) → (1) 25 Also Given x+y = 100 × (x2 − y2 ) 1 ⇒ x+y = 4 × (x2 − y2 ) ⇒ x2 − y2 = 4(x+y) → (2) Adding equation(1) and equation(2) ⇒ 2x2 = 9(x+y) x+y 2 x+y x2 is equal to ∴ x+y 2 x2 = 9