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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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Joined: 02 Sep 2009
Posts: 61283
If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is the value of  [#permalink]

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10 Jun 2019, 03:35
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75% (01:32) correct 25% (01:12) wrong based on 81 sessions

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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

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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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10 Jun 2019, 04:21
Top Contributor
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: $$6xy = 25$$

Cheers,
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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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

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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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