Problem Solving

Q. If x<0, simplify the given expression in terms of x,

[(x-3)^4]^1/4+(-x*absolute value of x)^1/2=?

IMO : 2X-3

((x-3)^4)^1/4 = (x-3)

(-x|x|)^1/2

Since x<0 , -x will be same as x
|x| will be = x,even though x is -ve

Hence,(-x|x|)^1/2 = (x^2)^1/2 = x

hence, x-3+x = 2x-3

NO the correct answer is 3-2x

Can Someone help?
Not sure where I went wrong!

Sanjana,

Your solution is also right but if it is not there as one of our answer options, we'll have to check if there is any other way to solve the equation.

Now,

((x-3)^4)^1/4 = (x-3) or (3-x)

Thats because (x-3)^4 = (3-x)^4

Similarly (-x|x|)^1/2 = x or -x

So, ((x-3)^4)^1/4 + (-x|x|)^1/2 can two solutions.

1) x-3+x = 2x-3
2) 3-x-x = 3-2x

The answer choice should have any one of these.

Hope I am clear.