Question

The sum of two positive numbers x and y (x > y) is 50 and the difference of their squares is 720. Find the numbers.

Answer 1

Two numbers are x and y such that x > y.

x + y = 50       ...(i)

x² - y² = 720

⇒ (x + y)(x - y) = 720

⇒ 50(x - y) = 720   ...[Using equation (i)]

⇒ x - y = `720/50`

⇒ x - y = 14.4                     ….(ii)

Adding (i) and (ii), we get

   x + y = 50
+ x - y = 14.4
2x = 64.4

x = `(64.4)/2`

⇒ x = 32.2

Substituting the value of x in (i), we have

x + y = 50

32.2+ y = 50

⇒ y = 50 - 32.2

⇒ y = 17.8

Thus, the two numbers are 17.8 and 32.2 respectively.