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pratu043

  • 3 years ago

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

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  1. sauravshakya
    • 3 years ago
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    IF n is odd

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

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

  4. pratu043
    • 3 years ago
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    What do you mean by that?

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

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

  7. pratu043
    • 3 years ago
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    ok

  8. pratu043
    • 3 years ago
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    So you should use factor theorem for this?

  9. sauravshakya
    • 3 years ago
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    yep

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

  11. pratu043
    • 3 years ago
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    ok got that.

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

  13. pratu043
    • 3 years ago
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    ok

  14. sauravshakya
    • 3 years ago
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    which is only possible when n is odd

  15. sauravshakya
    • 3 years ago
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    got it?

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

  17. sauravshakya
    • 3 years ago
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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

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