Posted by **luke** on Thursday, May 3, 2007 at 9:21pm.

I have no clue how to do this as no values were given and im confused. can someone explain plz?

if x^3-y^3=m and x-y=N, express xy in terms of M and N

This is one of those pure manipulation problems.

you have to know that x^3-y^3 = (x-y)(x^2+xy+y^2)

so n(x^2+xy+y^2)=m

(x^2+xy+y^2) = m/n (#1)

notice we have xy, which is what we want, inside the bracket, but there is that x^2+y^2 hanging around

(from countless years of experience I know)

x^2+y^2 = (x-y)^2 + 2xy

so let's put that back in #1

((x-y)^2 + 2xy + xy) = m/n

n^2 + 3xy = m/n

3xy = m/n - n^2

3xy = (m-n^3)/n

and finally

xy = (m-n^3)/(3n)

I don't know what grade level you are in but that is pretty nasty.

## Answer This Question

## Related Questions

- Math - Write two numbers that have the given absolute value. 4 38 260 4092 I ...
- Calc - Express the limit as a definite integral on the given interval. Use ...
- Calculus - Suppose f(x) is a differentiable function with f(-1)=2 and f(2)=-1. ...
- Calc - Use a table of values to estimate the value of the limit. lim (tan 3x/tan...
- math 012 please help explain - can someone please help explain how to do this ...
- Math - An angle ? satisfies the relation csc ? cos ? = -1. A) Use the definition...
- Pre-Algebra [repost ] - I need help on these three questions BEFORE 10:00 PM. ...
- Urgent Chem help plz - is answer +103 KJ.. plz chk Plz explain in detail.... i ...
- trig - Verify that each equation is an identity. 16. 1+tanx/sinx+cosx =secx ok i...
- confused - as i earlier posted and , 1 day ago , i am confusesd hw we ll find ...

More Related Questions