SOLUTION: if x plus y = a and xy = b, then the value of 1/x to the power of 3 plus 1/y to the power of 3 is equal to ?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: if x plus y = a and xy = b, then the value of 1/x to the power of 3 plus 1/y to the power of 3 is equal to ?      Log On


   

Question 935200: if x plus y = a and xy = b, then the value of 1/x to the power of 3 plus 1/y to the power of 3 is equal to ?
Found 3 solutions by josgarithmetic, MathLover1, Edwin McCravy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2Fx%29%5E3%2B%281%2Fy%29%5E3

%28y%5E3%2Bx%5E3%29%2F%28xy%29%5E3, and one of your equations gives you xy=b, so you can substitute:

%28x%5E3%2By%5E3%29%2Fb%5E3;

A formula is for the sum of cubes. You could try polynomial division to find it.
The formula in general: a%5E3%2Bb%5E3=%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29

Back to your expression,
%28x%2By%29%28x%5E2-xy%2By%5E2%29%2Fb%5E3, and you were given x+y=a;
highlight%28a%28x%5E2-b%2By%5E2%29%2Fb%5E3%29.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
if x+%2By+=+a and xy+=+b, then
x+=+a-yand y+=+b%2Fx
the value of 1%2Fx%5E3+%2B+1%2Fy%5E3
= 1%2F%28a-y%29%5E3+%2B+1%2F%28b%2Fx%29%5E3
=1%2F%28a-y%29%5E3+%2B+x%5E3%2Fb%5E3
=%28b%5E3+%2B+x%5E3%28a-y%29%5E3%29%2F%28%28a-y%29%5E3b%5E3%29
=
=

Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
The other two tutors above gave INCORRECT answers 
because they didn't know that you are not supposed 
to have x's and y's in the final answer, but only 
a's and b's.

if x plus y = a and xy = b, then the value of 1/x to the power of 3 plus 1/y to the power of 3 is equal to ?
system%28x%2By=a%2C%0D%0Axy+=+b%29

 

Now we need to find x%5E2%2By%5E2.  We square both side of

x%2By=a

x%5E2%2B2xy%2By%5E2=a%5E2

x%5E2%2B2b%2By%5E2=a%5E2

x%5E2%2By%5E2=a%5E2-2b

So

 

answer:

a%28a%5E2-3b%29%2Fb%5E3 

Edwin