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
