shrive555 wrote:

What is the value of x?

(1) \sqrt{x^4} = 9

(2) \sqrt{x^2}=-x

Responding to a pm:

**Quote:**

how to solve second statement? i did 2nd statement squaring on both sides then got same x^2 = x^2. then what to do after this?? and also how to solve combining both 1 and 2 statement??

Squaring is not the solution for every problem. When you square both sides you sometimes lose valuable information. e.g.

x = -5

Square -> x^2 = 25

If you are given x^2 = 25, all you can say is that x is 5 or -5. You cannot say which one. So you lost information here.

As for this question, there is a concept that you need to use here

\sqrt{x^2}= |x|\sqrt{9} = 3. It is not 3 or -3. Only the positive value is considered for square roots. Hence, the mod is used when dealing with a variable.

So from the second statement, you get |x| = -x

Now, we know that |x| = -x when x is negative. So the only thing that the second statement tells us is that x is negative.

Statement 1 tells you that x is 3 or -3. Statement 2 tells you that x is negative. SO using both statements, you can say that x = -3. Sufficient.

Answer (C)

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Karishma

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