Question

The difference between two numbers is 9 and the product of the two is 14.What is the square of their sum?

Answer 1

Let the 2 numbers be x and y
According to the problem,
x-y=9
xy=14
(x+y)square=?

xy=14
y=14÷x
Substitute the value of y for x-y=9
x-14÷x=9
( x square -14)÷x=9
x square-14=9x
x square-9x-14=0

x square-7x+2x-14=0
x(x-7)+2(x-7)=0
(x+2)(x-7)=0
x= -2,7
now xy=14
(-2)y=14
y= -7
So,(x+y)square=[-2+(-7)]square
=[-2-7]
=-9
Therefore,the square of their sum is -9

HOPE THIS HELPS