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pratu043 Group Title

Find the condition that x^n + y^n may be divisible by x + y.

  • 2 years ago
  • 2 years ago

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  1. sauravshakya Group Title
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    IF n is odd

    • 2 years ago
  2. pratu043 Group Title
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    How do you prove that?

    • 2 years ago
  3. Libniz Group Title
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    sum of odd roots factor always factor out (x+y)

    • 2 years ago
  4. pratu043 Group Title
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    What do you mean by that?

    • 2 years ago
  5. sauravshakya Group Title
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    I know how, PLZ wait sec trying to write it down

    • 2 years ago
  6. sauravshakya Group Title
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    Oh got it.... let f(x)=x^n + y^n

    • 2 years ago
  7. pratu043 Group Title
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    ok

    • 2 years ago
  8. pratu043 Group Title
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    So you should use factor theorem for this?

    • 2 years ago
  9. sauravshakya Group Title
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    yep

    • 2 years ago
  10. sauravshakya Group Title
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    now, when f(x) is divided by (x+y) then REMAINDER = f(-y) = (-y)^n + y^n

    • 2 years ago
  11. pratu043 Group Title
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    ok got that.

    • 2 years ago
  12. sauravshakya Group Title
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    Now, for x^n + y^n to be divisible by x + y.. remainder = 0 or, (-y)^n + y^n=0

    • 2 years ago
  13. pratu043 Group Title
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    ok

    • 2 years ago
  14. sauravshakya Group Title
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    which is only possible when n is odd

    • 2 years ago
  15. sauravshakya Group Title
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    got it?

    • 2 years ago
  16. pratu043 Group Title
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    ok so when n is odd, (-y)^n = -y so (-y)^n + y^n = -y + y = 0 thanks!!

    • 2 years ago
  17. sauravshakya Group Title
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    oh its like this: when n is odd, (-y)^n = -(y)^n so (-y)^n + y^n = -(y)^n + y^n = 0

    • 2 years ago
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