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Difficulty:
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Question Stats:
58% (02:26) correct
42%
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If x and y are positive and x^2*y^2=18-3xy, then x^2 =
A. (18-3y)/y^3
B. 18/y^2
C. 18/(y^2+3y)
D. 9/y^2
E. 36/y^2
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-positive-and-x-2y-2-18-3xy-then-x-140728.html
A. (18-3y)/y^3
B. 18/y^2
C. 18/(y^2+3y)
D. 9/y^2
E. 36/y^2
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-positive-and-x-2y-2-18-3xy-then-x-140728.html
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17 Oct 2010, 06:45
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samark
\(x^2y^2+3xy-18=0\)
\((xy+6)(xy-3)=0\)
So xy=3 or xy=-6
But x and y are positive, so xy=3
Hence, x^2=9/y^2
Answer is (d)
17 Oct 2010, 06:48
Kudos
Bookmarks
If x and y are positive and x^2*y^2=18-3xy, then x^2 =
A. (18-3y)/y^3
B. 18/y^2
C. 18/(y^2+3y)
D. 9/y^2
E. 36/y^2
\((xy)^2+3(xy)-18=0\) --> solving for \(xy\) --> \(xy=-6\) (not a valid solution: \(xy\) must be positive as both unknowns are positive) or \(xy=3\) --> so \(xy=3\) --> \(x=\frac{3}{y}\) --> \(x^2=\frac{9}{y^2}\).
Answer: D.
A. (18-3y)/y^3
B. 18/y^2
C. 18/(y^2+3y)
D. 9/y^2
E. 36/y^2
\((xy)^2+3(xy)-18=0\) --> solving for \(xy\) --> \(xy=-6\) (not a valid solution: \(xy\) must be positive as both unknowns are positive) or \(xy=3\) --> so \(xy=3\) --> \(x=\frac{3}{y}\) --> \(x^2=\frac{9}{y^2}\).
Answer: D.
