sqrt((x-5)^2) = 5-x?

sqrt((x-5)^2) = |x-5|
|x-5| = 5-x

The above equation has two values
x-5 = 5-x or -(x-5) = 5-x depending on whether (x-5) > or < 0

1. -x|x| > 0
the above is possible only for x < 0, therefore (x-5) < 0
So |x-5| = 5-x => -(x-5) = 5-x.

SUFF

2. States that (x-5) < 0

SUFF

IMO D

(D)

sam2304 wrote:sqrt((x-5)^2) = 5-x?

sqrt((x-5)^2) = |x-5|
|x-5| = 5-x

The above equation has two values
x-5 = 5-x or -(x-5) = 5-x depending on whether (x-5) > or < 0

1. -x|x| > 0
the above is possible only for x < 0, therefore (x-5) < 0
So |x-5| = 5-x => -(x-5) = 5-x.

SUFF

2. States that (x-5) < 0

SUFF

IMO D

I think the answer should be A..

Question asks:

is sqrt((x-5)^2) = 5-x

so...is |x-5| = 5-x

so the question basically is asking is x < 0

because only then will |x-5| = 5 - x

so... Now the question becomes is x < 0

Statement A:

-x|x| > 0

which means that x has to be negative since |x| is positive

hence -x |x| will only be positive if x is negative...

hence Sufficient

Statement B:

(5-x) > 0

Which basically means x < 5

So x could be positive and could be negative..

Hence Insufficient..

Answer has to be A

Whats the original answer?

Yes Chufus is right!!! THe second equation cannot only x < 0

Let us solve the equation : (5-x) > 0

Subtracting by 5 on both sides

-x > -5,

Multiplying by (-1) on both sides,

hence x < 5


hence the x can be < 0 also and (0 < x < 5) is also possible. So statement 2 becomes insufficient

No no the answer should be D and not A.

As the question is asking us whether |x-5| = (5-x)

For this to happen, either x < 0 or 0 < x < 5, both the equations are correct.
Basically x should be < than 5.

So both the equations are correct.

got confused...

Chufus hope this helps man...

kishokbabu wrote:Is √((x-5)^2) = (5-x) ?

1) -x|x| > 0
2) (5-x) > 0

√x² = |x|.

Thus, the question is asking Is |x-5| = 5-x?
The CRITICAL POINT is x=5: this is where x-5 changes sign.

Case 1: x<5.
When x<5, x-5<0.
Since |x-5| cannot be negative, x-5 must be replaced by 5-x:
5-x = 5-x
0 = 0.
This means that the value of x here is irrelevant: ANY value will work.
Thus, the entire range x<5 satisfies |x-5| = 5-x.

Case 2: x≥5.
In this range, x-5≥0, so the expression does not have to be rewritten.
x-5 = 5-x
2x = 10
x = 5.
This means that the ONLY allowed value in this range is x=5.

Thus, the total range of values that satisfies |x-5| = 5-x is x≤5.

Question rephrased: Is x≤5?

Statement 1: -x|x| > 0.
The expression above is valid only if x<0, so that the expression becomes:
-(negative) * |negative| > 0
positive * positive > 0.
Since x<0, we know that x≤5.
SUFFICIENT.

Statement 2: 5-x > 0.
x<5.
SUFFICIENT.

The correct answer is D.