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rommysingh
- Master | Next Rank: 500 Posts
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x²y² = 18 - 3xy = (xy)² = 18 - 3xyIf 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
To make it easier to solve this equation, let k = xy
We get: k² = 18 - 3k
Rewrite as: k² + 3k - 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
