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If √x+√y=7 and √x-√y=5, what is the value of xy?

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If √x+√y=7 and √x-√y=5, what is the value of xy?  [#permalink]

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New post 14 Mar 2019, 01:56
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[GMAT math practice question]

If \(√x+√y=7\) and \(√x-√y=5\), what is the value of \(xy\)?

\(A. 16\)
\(B. 25\)
\(C. 36\)
\(D. 49\)
\(E. 64\)
Spoiler: OA

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Re: If √x+√y=7 and √x-√y=5, what is the value of xy?  [#permalink]

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New post 14 Mar 2019, 02:20
It's given the system of two linear equations:

\(\sqrt{x} + \sqrt{y} = 7\)

\(\sqrt{x} - \sqrt{y} = 5\)

Subtraction method gives: \(2\sqrt{y} = 2\)

Hence, \(y = 1\)

Substitute the variable into one of the two linear equations to state the value of \(x\).

If we take the first one, \(\sqrt{x} + 1 = 7\)

\(x = 36\)

As a result, \(xy = 36\)
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Re: If √x+√y=7 and √x-√y=5, what is the value of xy?  [#permalink]

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New post 14 Mar 2019, 02:22
√x+√y=7...i) and √x-√y=5...ii)

Adding i) & ii), we get

2√x=12
=> √x = 6
=> x = 36

Substituting the value in i) we get,

√y = 1
=> y = 1

So xy = 36

Option C) is the answer
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Re: If √x+√y=7 and √x-√y=5, what is the value of xy?  [#permalink]

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New post 14 Mar 2019, 02:57
MathRevolution wrote:
[GMAT math practice question]

If \(√x+√y=7\) and \(√x-√y=5\), what is the value of \(xy\)?

\(A. 16\)
\(B. 25\)
\(C. 36\)
\(D. 49\)
\(E. 64\)



Given,

\(√x+√y=7\)

\(√x-√y=5\)

...........................................Adding both equation .
2√x = 12

√x = 6

Substitute the value of √x into equation 1.

6 + √y = 7

√y = 1


Now are looking for the value of xy.


√x√y = 6*1

\(\sqrt{xy}\) = 6

xy = 36.

C is the correct answer.
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Re: If √x+√y=7 and √x-√y=5, what is the value of xy?  [#permalink]

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New post 17 Mar 2019, 18:18
=>

Adding the two equations yields \(2√x = 12\), so \(x = 36.\)
Subtracting the two equations yields \(2√y = 2\), so \(y = 1\).
Therefore, \(xy = 36\).

Therefore, the answer is C.
Answer: C
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Re: If √x+√y=7 and √x-√y=5, what is the value of xy?   [#permalink] 17 Mar 2019, 18:18
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