Math

posted by .

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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. trig

    Verify that each equation is an identity. 16. 1+tanx/sinx+cosx =secx ok i have a clue on how to do it. i multiplyed the denominator by sinx-cosx and i also did the top but when i do i get this weird fraction with all these cos and …
  2. Urgent Chem help plz

    is answer +103 KJ.. plz chk Plz explain in detail.... i tried to search on internet but i am confused with co-efficents.. how to set up the equaiton .. plz help me ?
  3. math 012 please help explain

    can someone please help explain how to do this problem. i have a previous posting where i tried to work the problem out, and someone tried to explain where i was confused, but im still confused. 4(2n+1)=3(6n+3)+1
  4. Pre-Algebra [repost ]

    I need help on these three questions BEFORE 10:00 PM. Please someone show me how to do them step by step! Solve the equation for y in terms of x then find the solutions of the equation for the given values of x. 1.x + y = -1 [values …
  5. Calc

    Use a table of values to estimate the value of the limit. lim (tan 3x/tan 5x) x--> 0 I have no clue what to do. Could someone please explain how to go about this problem.
  6. Calc

    Express the limit as a definite integral on the given interval. Use Riemright and evaluate the sum by hand. lim n-> infinity sigma with n on top and i=1 on the bottom [4 - 3(xi*)^2 + 6(xi*)^5]delta x, [0,2] Please help. I am really …
  7. Math

    Write two numbers that have the given absolute value. 4 38 260 4092 I know one is 4 but do not know the second unless it is -4 Do not have no clue can someone explain?
  8. chemistry

    write the corresponding subshell leters for the combinations given. Fill in the possible number of electrons for these subshells. 1) n=1 2) l value=0 3) l letter?
  9. Calculus

    Suppose f(x) is a differentiable function with f(-1)=2 and f(2)=-1. The differentiable function g(x) is defined by the formula g(x)=f(f(x))' A. Compute g(-1) and g(2). Explain why g(x)=0 must have at least one solution A between -1 …
  10. Math

    An angle θ satisfies the relation csc θ cos θ = -1. A) Use the definition of the reciprocal trigonometric ratios to express the left side in terms of sin θ and cos θ. B) What is the relation between sin θ and cos θ for this …

More Similar Questions