If X and Y are positive, which of the following must be greater than 1/(x+y)^5?
1. (x+y)^5 / 2x
2. [(x^5) + (y^5)]/(x+y)
3. [(x^5) - (y^5)]/(x+y)
The OA is [spoiler]2 only[/spoiler]. I agree with 2 being greater than 1/(x+y)^5 but I'm getting 1 also as greater than 1/(x+y)^5. I agree with 3 not being greater than 1/(x+y)^5.
Here is how I'm getting 1 greater than 1/(x+y)^5
I have the habit of solving such fraction comparison problems by cross multiplication.
For 1.
(x+y)^5/2x and 1/(x+y)^5
Cross multiplying we get,
(x+y)^10 and 2x
Since x and y are positive left side is going to be greater than right side. Also if x=y then we would have
(2x)^10 and 2x. Left hand side is greater than right. So why is 1 not greater than 1/(x+y)^5?
1. (x+y)^5 / 2x
2. [(x^5) + (y^5)]/(x+y)
3. [(x^5) - (y^5)]/(x+y)
The OA is [spoiler]2 only[/spoiler]. I agree with 2 being greater than 1/(x+y)^5 but I'm getting 1 also as greater than 1/(x+y)^5. I agree with 3 not being greater than 1/(x+y)^5.
Here is how I'm getting 1 greater than 1/(x+y)^5
I have the habit of solving such fraction comparison problems by cross multiplication.
For 1.
(x+y)^5/2x and 1/(x+y)^5
Cross multiplying we get,
(x+y)^10 and 2x
Since x and y are positive left side is going to be greater than right side. Also if x=y then we would have
(2x)^10 and 2x. Left hand side is greater than right. So why is 1 not greater than 1/(x+y)^5?
