Question

If xy = 144, x + y = 30, and x > y, what is the value of x – y ?

Answer 1

The value of x-y is 18

Explanation:

From the question, we can deduced the following ;

xy = 144....eqn(1)

x+y=30.......eqn(2)

For eqn(2), we subtract y from both sides to make x the subject.

`\implies x + y - y= 30 - y`

`\implies x= 30 - y`

Putting that x=30-y into eqn(1) we obtain;

`y(30 - y)=144`

`\implies 30y - {y}^(2) =144`

`\implies 0= {y}^(2) - 30 + 144`

`\implies 0= {y}^(2) - 24y - 6y+ 144`

`\implies 0=y(y- 24)- 6(y - 24)`

`\implies 0=(y- 6)(y - 24)`

This implies that

y-6=0 or y-24=0

Hence, y=6 or y=24.

Therefore, when x=6 then y=24 and when x=24, then y=6 all satisfy the given equations.

But from the question, x>y.

This implies that,x=24 and y= 6

Thus, the value of x-y=24-6=18