roots - exponents - absolutes

I would go with C)

I am asuming = sign is missing in the diagram

sqrt(|x|) ^ 2 is |x| which is x if x is positive or 0

Stmt II

x^0 = 1

x can be positive or negative

INSUFF

Toegther x has to be psoitive since 0^0 is not equal to 1

Statement I

(sqrtlxl)^2 = x

if x = -1

lxl = 1

(sqrt 1)^2 = 1 but this is not equal to x, which is -1

Hence only way this could be possible when x = positive.

Sufficient

Statement II

x^0 = 1

irrespective of any value of x, any value when raised to the power of 0 will always result in 1, Therefore x could be positive or negative.

Insufficient.

Hence A.

PC I thought of A too initially then decided C) for reasons posted above.

Let me know what u think

cramya wrote:PC I thought of A too initially then decided C) for reasons posted above.

Let me know what u think

Nice work cramya, missed that 0, I hate to make silly mistakes.

Answer should be C.

I also have a doubt in statement II

-2^0 = -1

2^0 = 1

are these correct or is it I am right in my logic to assume that any number positive or negative, when raised to the power of 0 is 1.

thanks.

I also have a doubt in statement II

-2^0 = -1

2^0 = 1

are these correct or is it I am right in my logic to assume that any number positive or negative, when raised to the power of 0 is 1

PC its always 1.

-2^0 = 1

2^0 = 1

cramya wrote:

I also have a doubt in statement II

-2^0 = -1

2^0 = 1

are these correct or is it I am right in my logic to assume that any number positive or negative, when raised to the power of 0 is 1

PC its always 1.

-2^0 = 1

2^0 = 1

Thanks Buddy.

pls tell me ...cramya...howcm u arrvied it on...pls elaborate...
i face too much prob in absolute values.

pls elaborate ur sol.

cramya wrote:
sqrt(|x|) ^ 2 is |x| which is x if x is positive or 0

This is creating probs. as u said , sqrt(|x|) ^ 2 is |x|
now it boils down to |x| =x
now if x is +ve it holds
if x is -ve, then LHS = x and RHS = -x , not equal....


why and hw u hv taken 0 in consideration is my ques.

why and hw u hv taken 0 in consideration is my ques

Hi Vivek,

Basic but important piece of information:

The absolute value(never negative) or magnitude of a real number x is denoted
by |x| and is defined by

|x| = x if x ≥ 0 ( x is greater than or equal to 0)
|x| = &#8722;x if a < 0

stmt I tells us it either a 0 or a positive number. Hence INSUFF

Together it cant be 0 since 0^0 is undefined so has to be a positive number


Hope this helps!