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let me do this way. first simplify the question. remember this is yes/no question.

given that sqrt[(x-5)^2] = 5-x is equivalant to x=5? because sqrt [(x-5)^2] = x-5 (because sqrt of something is always positive. so it is x-5).
so the enequality is x-5 = 5-x......after simplification, x=5.

i) -x|x|>0
from this, x is -ve. so x is definitely not 5. sufficient...............

ii) 5-x>0. Please explain.
from ii, 5>x. this also means x is not equal to 5. it is also sufficient............

1) From statement 1, we get x to be negative. I tried substituting the original formulas, for various numbers, and the base statement was true. Hence statement 1 is sufficient.

2) From statement 2, we get X < 5. I substituted x to be a positive number less than 5, and a negative number, and the statement still holds good.

Hence my answer was D.

But having looked at your post, felt there was a better way of doing it. Thanks.

what if we rewrite it as (x-5)^2=(5-x)^2, and then it would mean (x-5)^2=(-(x-5))^2, right? (x-5)^2=(x-5)^2 thus, it might be concluded that x can be any number, which makes the answer D since it does not really matter what they put in st1 or st2.

because sqrt [(x-5)^2] = x-5 (because sqrt of something is always positive. so it is x-5). ..

I didn't understand what u mean by that Sqrt (9) = +- 3 rt? Kindly explain. Saurabh Malpani

saurabh, Sqrt (9) = always and only +3 not -3.

Can you figure out if there are any flaws in my reasoning? That would be of great help to me.....Also suggestions on where to find more "Inequalities" problems....

This question is from OG. Is sqrt[(x-5)^2] = 5-x? i) -x|x|>0 ii) 5-x>0

Please correct my approach if it is wrong. I am having some confusion with this problem. From 1) since |x| is always positive -x|x| > 0 only if x<0 ==>> sqrt[(x-5)^2] = 5-x means (x-5)<0 from 2) 5-x>0 means (x-5)<0 So we can get from 1 and 2 . Is this approach correct??

i think, there is nothing wrong with your approach. you only did not simplified the given inequality in the question. if the given inequality is complex and multiple variables, it better to simplify to the possible extent. if you simplifiy the question, you can get the answer.

This question is from OG. Is sqrt[(x-5)^2] = 5-x? i) -x|x|>0 ii) 5-x>0

Please correct my approach if it is wrong. I am having some confusion with this problem. From 1) since |x| is always positive -x|x| > 0 only if x<0 ==>> sqrt[(x-5)^2] = 5-x means (x-5)<0 from 2) 5-x>0 means (x-5)<0 So we can get from 1 and 2 . Is this approach correct??

i think, there is nothing wrong with your approach. you only did not simplified the given inequality in the question. if the given inequality is complex and multiple variables, it better to simplify to the possible extent. if you simplifiy the question, you can get the answer.