SOLUTION: If x/y + y/x= a and x/y - y/x= b, then the value of (a square - b square) is equal to-

Algebra ->  Expressions-with-variables -> SOLUTION: If x/y + y/x= a and x/y - y/x= b, then the value of (a square - b square) is equal to-      Log On


   

Question 822588: If x/y + y/x= a and x/y - y/x= b, then the value of (a square - b square) is equal to-
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
x%2Fy+%2B+y%2Fx=+a and x%2Fy+-+y%2Fx=+b
We're looking for the value of a%5E2-b%5E2

Probably the easiest way to figure this out is to recognize that there is a factoring pattern with a%5E2-b%5E2 in it:
a%5E2-b%5E2+=+%28a%2Bb%29%28a-b%29

To find a%5E2-b%5E2 we will figure out what (a+b)(a-b) works out to be. Substituting the given expressions for a and b into (a+b)(a-b) we get:

Note the use of parentheses! It is critical to use them like this when substituting in complex expressions.

Now we simplify. In the a+b factor the y/x's cancel and in the a-b factor the x/y's cancel:
%282x%2Fy%29%282y%2Fx%29
Now when we multiply the x's cancel and the y's cancel leaving us with:
2*2 or 4