The product of two positive numbers is 32. If the sum of their squares is 80, then find the difference between the two numbers

The product of two positive numbers is 32. If the sum of their squares is 80, then find the difference between the two numbers.

a)            12

b)            14

c)            4

d)            8

e)            10

Sol:

Let the two numbers be ‘a’ and ‘b’.

a*b = 32 ……………. (1)

a² + b² = 80 …………… (2)

We know that (a – b)² = a² + b² – 2ab

Equation (1), (2)

(a – b)² = 80 – 2 *32

(a – b)² = 16

a – b = 4

Required difference = 4