Question

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

Answer 1

`x-y=color(green)(18)`

Explanation:

Given
[1]`color(white)("XXX")xy=144`
[2]`color(white)("XXX")x+y=30color(white)("X")rarrcolor(white)("X")y=30-x`

Substituting `(30-x)` for `y` back in [1]
[3]`color(white)("XXX")x(30-x)=144color(white)("X")rarrcolor(white)("X")x^2-30x+144=0`

Factoring
[4]`color(white)("XXXXXXXXXXXXXXXXX")(x-6)(x-24)=0`

Either `x=6` or `x=24`

[1] and [2] are symmetric, so whichever value is assigned to `x`, the other value is assigned to `y`

and since we are told `x > y`
`color(white)("XXX")rarr x=24 and y=6`

`rArr x-y = 24-6=18`