Sum of two integers and their product is 90. If both the integers are greater than 1, then find the difference between the square

Sum of two integers and their product is 90. If both the integers are greater than 1, then find the difference between the square of these two integers.

a) Cannot be determined

b) 108

c) 120

d) 90

e) 96

Sol:

Let integers be ‘x’ and ‘y’ (x > y).

According to the question:

x + y + xy = 90

Add ‘1’ on both sides:

1 + x + y + xy = 90 + 1

(1 + x) (1 + y) = 91

(1 + x) (1 + y) = 13 * 7

After comparing:

x = 12 and y = 6

Difference between square of two integers = 12²– 6² = 108