If x and y are positive and x²y² = 18 - 3xy, then x² =
A) (18 - 3y)/y³
B) 18/y²
C) 18/(y² + 3y)
D) 9/y²
E) 36/y²
x²y² = 18 - 3xy = (
xy)² = 18 - 3
xy
To make it easier to solve this equation, let
k =
xy
We get:
k² = 18 - 3
k
Rewrite as:
k² + 3
k - 18 = 0
Factor: (
k + 6)(
k - 3)
So, EITHER
k = -6 OR
k = 3
This means that EITHER
xy = -6 OR
xy = 3
case a:
xy = -6
Since x and y are both POSITIVE,
xy cannot equal -6.
So, we can rule out case a.
case b:
xy = 3
Since x and y are both POSITIVE, it's possible for
xy to equal 3.
If
xy = 3, then (
xy)² = 3²
Simplify to get: x²y² = 9
Divide both sides by y² to get: x² = [spoiler]9/y²[/spoiler]
Answer:
D
Cheers,
Brent
