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mathmath333

  • one year ago

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  1. mathmath333
    • one year ago
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    if \(\large \color{black}{\begin{align} f(x+y,x-y)=xy \hspace{1.5em}\\~\\ \end{align}}\) find \(\large \color{black}{\begin{align} f(x,y)=? \hspace{1.5em}\\~\\ \end{align}}\)

  2. anonymous
    • one year ago
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    ok, have you tried it yet?

  3. mathmath333
    • one year ago
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    yes

  4. anonymous
    • one year ago
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    what did you get?

  5. mathmath333
    • one year ago
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    wait

  6. mathmath333
    • one year ago
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    i replaced x+y=a , x-y=b and got \(f(a,b)=ax-ab-yx+yb\)

  7. anonymous
    • one year ago
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    very good, now eliminate a and b on the RHS

  8. mathmath333
    • one year ago
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    how do i eliminate that ?

  9. anonymous
    • one year ago
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    sry eliminate x and y, well you can find x and y in terms of a and b

  10. mathmath333
    • one year ago
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    i have a question , can i just replace a and b by 'x' and 'y' \(f(a,b)=ax-ab-yx+yb\\ f(x,y)=x^2-xy-yx+y^2=(x-y)^2\)

  11. anonymous
    • one year ago
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    emm no, look at to your first substitution

  12. mathmath333
    • one year ago
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    ok

  13. mathmath333
    • one year ago
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    i got x=(a+b)/2, y=(a-b)/2 is that correct substitution

  14. anonymous
    • one year ago
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    that's right, put those back in the f(a,b)

  15. mathmath333
    • one year ago
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    got \(f(a,b)=\dfrac{a^2-b^2}{4}\)

  16. anonymous
    • one year ago
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    we're done

  17. mathmath333
    • one year ago
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    i put now (a,b)-> (x,y) ?

  18. anonymous
    • one year ago
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    yes :-)

  19. mathmath333
    • one year ago
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    oh thnx

  20. anonymous
    • one year ago
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    np math

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