Question

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

Answer 1

Answer:

The value of x-y is 18

Step-by-step 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