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JEE Delight | B Stat/ B Math | ISI | UGB 2023 | Q7 | Complex numbers | X^n+Y^n+Z^n
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JEE Delight | B Stat/ B Math | ISI | UGB 2023 | Q7 | Complex numbers | X^n+Y^n+Z^n
Prove that Xn +Y
n +Z
n can be written as
a polynomial with integer coefficients in the variables α = X + Y +
Z, β = XY + Y Z + ZX and γ = XY Z.
(b) Let Gn = xnsin(nA)+ynsin(nB)+znsin(nC), where x, y, z, A, B, C
are real numbers such that A + B + C is an integral multiple of π.
Using (a) or otherwise, show that if G1 = G2 = 0, then Gn = 0 for
all positive integers n
Support the channel:
Prove that Xn +Y
n +Z
n can be written as
a polynomial with integer coefficients in the variables α = X + Y +
Z, β = XY + Y Z + ZX and γ = XY Z.
(b) Let Gn = xnsin(nA)+ynsin(nB)+znsin(nC), where x, y, z, A, B, C
are real numbers such that A + B + C is an integral multiple of π.
Using (a) or otherwise, show that if G1 = G2 = 0, then Gn = 0 for
all positive integers n
Support the channel:
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