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Pls answer this question . pls dont post replies like - i dont know |
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Answer» a = a, BETA = b given, a and b are roots of x^2 + px + q = 0 means x = a or x = b also a + b = -p ab = q again a and b are roots of x^2n + p^N x^n + q^n = 0 means x = a or x = b so x^n = a^n or x^n = b^n now, x^2n + p^n x^n + q^n = 0 (x^n)^2 + p^n x^n + q^n = 0 this is a quadratic equation whose roots are x^n = a^n or x^n = b^n so sum of roots = -p^n a^n + b^n = - p^n a^n b^n = q^n now a/b , b/a are roots of (x + 1)^n + x^n + 1 = 0 putting x = a/b we get (a/b + 1)^n + (a/b)^n + 1 = 0 (a + b)^n / b^n + a^n / b^n + 1 = 0 (a + b)^n + a^n + b^n = 0 ( if we keep x = b/a in the equation, we will get the same expression as above) so in both cases (a + b)^n + a^n + b^n = 0 now a+ b = -p a^n + b^n = -p^n thus ( - p )^n + (- p^n) = 0 ( - p )^n - p^n = 0 since we have put the roots in the equation, the VALUE must be zero.. since p is not zero, for the value to be equal to zero ( - p )^n should be equal to p^n this is possible only when n is EVEN |
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