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For all positive numbers x and y, the operation x ♦ y is defined by x

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Math Expert
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For all positive numbers x and y, the operation x ♦ y is defined by x  [#permalink]

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New post 19 Mar 2020, 08:07
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

87% (01:02) correct 13% (01:53) wrong based on 39 sessions

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For all positive numbers x and y, the operation x ♦ y is defined by x  [#permalink]

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New post 19 Mar 2020, 08:15
Bunuel wrote:
For all positive numbers x and y, the operation \(x ♦ y\) is defined by \(x ♦ y = \frac{x^2 - x}{2xy}\). If \(x ♦ 5 = 2\), then \(x =\)

A. 1
B. 5
C. 11
D. 20
E. 21


Asked; For all positive numbers x and y, the operation \(x ♦ y\) is defined by \(x ♦ y = \frac{x^2 - x}{2xy}\). If \(x ♦ 5 = 2\), then \(x =\)

m]x ♦ y = \frac{x^2 - x}{2xy}[/m]
\(x ♦ 5 = \frac{x^2 - x}{10x} = 2\)
\(x^2 - x = 20x\)
\(x^2 - 21x = 0\)
x(x-21) = 0
x = 21 ; Since x <>0

IMO E
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Re: For all positive numbers x and y, the operation x ♦ y is defined by x  [#permalink]

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New post 19 Mar 2020, 08:46
1
For all positive numbers x and y, the operation \(x ♦ y\) is defined by \(x ♦ y = \frac{x^2 - x}{2xy}\). If \(x ♦ 5 = 2\), then \(x =\)

A. 1
B. 5
C. 11
D. 20
E. 21 --> correct: \(x ♦ 5 = (x^2 -x)/2*x*5= 2\) => x^2 -x = 20x => x^2-21x = 0 => x(x-21)=0 => x >0, so x =21
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Re: For all positive numbers x and y, the operation x ♦ y is defined by x  [#permalink]

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New post 20 Mar 2020, 12:39
21
x♦5=2
x^2-x/2.x.5=2
x^2-x=20x
x^2=21x
Hence x=21
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Re: For all positive numbers x and y, the operation x ♦ y is defined by x  [#permalink]

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New post 21 Mar 2020, 14:56
Bunuel wrote:
For all positive numbers x and y, the operation \(x ♦ y\) is defined by \(x ♦ y = \frac{x^2 - x}{2xy}\). If \(x ♦ 5 = 2\), then \(x =\)

A. 1
B. 5
C. 11
D. 20
E. 21


Since x * 5 = 2:

(x^2 - x) / [(2)(x)(5)] = 2

(x^2 - x) / (10x) = 2

x^2 - x = 20x

x^2 - 21x = 0

x(x - 21) = 0

x = 0 or x = 21

Since x is positive, x = 21.

Answer: E
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Re: For all positive numbers x and y, the operation x ♦ y is defined by x   [#permalink] 21 Mar 2020, 14:56

For all positive numbers x and y, the operation x ♦ y is defined by x

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