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If x^2+9+x^2-3=6, what is

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by Max@Math Revolution » Tue Feb 25, 2020 1:21 am

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[GMAT math practice question]
If \(\sqrt{x^2+9}+\sqrt{x^2-3}=6\) , what is \(\sqrt{x^2+9}-\sqrt{x^2-3}\) ?

A. 1
B. 2
C. 3
D. 4
E. 5
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Re: If x^2+9+x^2-3=6, what is

by Max@Math Revolution » Thu Feb 27, 2020 1:04 am
=>
\(\left(\sqrt{x^2+9}+\sqrt{x^2-3}\right)\left(\sqrt{x^2+9}-\sqrt{x^2-3}\right)\)
\(=\left(\sqrt{x^2+9}\right)\left(\sqrt{x^2+9}\right)-\left(\sqrt{x^2+9}\right)\left(\sqrt{x^2-3}\right)+\left(\sqrt{x^2-3}\right)\left(\sqrt{x^2+9}\right)-\left(\sqrt{x^2-3}\right)\left(\sqrt{x^2-3}\right)\) (by multiplying the 2 binomials)
= \(\left(x^2+9\right)-\left(x^2-3\right)\) (by simplifying)
= \(x^2+9-x^2-3\) (by multiplying -1 through the second bracket)
= 12

Then we have \(6\left(\sqrt{x^2+9}-\sqrt{x^2-3}\right)=12\) or \(\sqrt{x^2+9}-\sqrt{x^2-3}=2\) .

Therefore, B is the answer.
Answer: B
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