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If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is the value of

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If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is the value of  [#permalink]

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New post 10 Jun 2019, 03:35
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C
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Question Stats:

76% (01:32) correct 24% (01:12) wrong based on 84 sessions

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If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is the value of  [#permalink]

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New post 10 Jun 2019, 04:21
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Bunuel wrote:
If \(4x^2 + 9y^2 = 100\) and \((2x + 3y)^2 = 150\), then what is the value of \(6xy\)?

(A) 5(2 + √6 )

(B) 10√6

(C) 25

(D) 50

(E) 100


GIVEN: \((2x + 3y)^2 = 150\)

Expand and simplify to get: \(4x^2+12xy+9y^2 = 150\)
We're also given the equation: \(4x^2 + 9y^2 = 100\)

Subtract the bottom equation from the top equation to get: \(12xy = 50\)
Divide both sides by 2 to get: \(6xy = 25\)

Answer: C

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Brent
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Re: If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is the value of  [#permalink]

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New post 01 Jan 2020, 18:35
Bunuel wrote:
If \(4x^2 + 9y^2 = 100\) and \((2x + 3y)^2 = 150\), then what is the value of \(6xy\)?

(A) 5(2 + √6 )

(B) 10√6

(C) 25

(D) 50

(E) 100


FOILing the left hand side of the second equation, we have:

4x^2 + 9y^2 + 12xy = 150

Subtracting the first equation 4x^2 + 9y^2 = 100 from the equation above, we have:

12xy = 50

Dividing both sides of the equation by 2, we have:

6xy = 25

Answer: C
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Re: If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is the value of   [#permalink] 01 Jan 2020, 18:35
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