perplexus.info :: Just Math : Ratio Difference Crossed Value Determination

Ratio Difference Crossed Value Determination (Posted on 2023-09-26)

Each of x and y is a real number that satisfies this equation:

 1     1      1
--- - --- = -----
 x     2y    2x+y

Determine the value of:

 y²     x²
---- + ----
 x²     y²

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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solution

Comment 3 of 3 |

Simplify the first equation to get (x^2-y^2)=xy/2.

The second expression simplifies to (x^4+y^4)/(xy)^2 which can be recast as ((x^2-y^2)^2+2(xy)^2)/(xy)^2

Plug in the value from line 1 and after cancelling you're left with 1/4+2=9/4.

Posted by xdog on 2023-09-26 13:10:50

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