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)
I completely understand the above explanation but can you tell me why i cannot apply the below process,
statement ii.