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Equation with roots

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Source: — Problem Solving |
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Re: Equation with roots

by parallel_chase » Sun Dec 28, 2008 3:01 pm
Brent Hanneson wrote:Which of the following is a root of the equation sqrt(4x) = sqrt(x^2 - 21) ?

A) -3
B) -1
C) 3
D) 5
E) 7
sqrt(4x) = sqrt(x^2 - 21)

4x = x^2 -21

x^2 -4x -21 = 0

x =7 or -3

I think the answer should be 7 because if we take -3 then the equation becomes undefined.

Hence E.

Kindly correct me if I am wrong.
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by Brent@GMATPrepNow » Sun Dec 28, 2008 3:03 pm
Correct as usual :D
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by vittalgmat » Mon Dec 29, 2008 12:43 am
remove the sqrt by squaring and solve the eqn to get 2 roots 7 and -3
Coz we have the original eqn under sqrt, we have one more step to do.

-3 cannot be the soln coz sqrt of -ve number is undefined.

Good Q
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by rajataga » Mon Dec 29, 2008 12:55 am
(x^2 - 21) cannot be negative....

hence, only possible answers are '5' or '7'

plugging in the values, you get answer 'E'
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