anonymous
  • anonymous
Find the condition that x^n + y^n may be divisible by x + y.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
IF n is odd
anonymous
  • anonymous
How do you prove that?
anonymous
  • anonymous
sum of odd roots factor always factor out (x+y)

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anonymous
  • anonymous
What do you mean by that?
anonymous
  • anonymous
I know how, PLZ wait sec trying to write it down
anonymous
  • anonymous
Oh got it.... let f(x)=x^n + y^n
anonymous
  • anonymous
ok
anonymous
  • anonymous
So you should use factor theorem for this?
anonymous
  • anonymous
yep
anonymous
  • anonymous
now, when f(x) is divided by (x+y) then REMAINDER = f(-y) = (-y)^n + y^n
anonymous
  • anonymous
ok got that.
anonymous
  • anonymous
Now, for x^n + y^n to be divisible by x + y.. remainder = 0 or, (-y)^n + y^n=0
anonymous
  • anonymous
ok
anonymous
  • anonymous
which is only possible when n is odd
anonymous
  • anonymous
got it?
anonymous
  • anonymous
ok so when n is odd, (-y)^n = -y so (-y)^n + y^n = -y + y = 0 thanks!!
anonymous
  • anonymous
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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