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if x>y>0, which of the following must be true? I. [#permalink]
29 May 2007, 16:00
if x>y>0, which of the following must be true?
I. root(x) - root(y) < root(x-y)
II. x^2 - y^2 > (x-y)^2
2. I only
3. II only
4. I and II
5. Cannot be determined
If you can, please provide an ALGEBRAIC SOLUTION/DERIVATION/PROOF for the two inequations. I got some answers after testing with several numbers - but it took a while and number plug-in method makes me unsure. Thanks.
i don't know of an algebraic/proof way to answer this q- there are some smart people on this board who might have a 'number theory' type of answer/explanation for you... but sometimes i think you just gotta plug in.
i think you can answer this quickly by picking an x and y value that satisfies the inequality (x is bigger than y, y is bigger than zero) and keeping the x and y the same acorss inequalities keeps it consistent
i pikced 100 and 36
you can estimate with fractions even:
I: 1/2-1/3 < square root 5/36
1/6 < use 4/36 instead (a smaller # but easy to find root of)