If x y - y x - - 1x-y 0 then x3 - y3

Given xy+yx= 1 #160; #160; #160; x^2+y^2= xy #160; #160; #160; x^2+y^2+xy=O Now #160; #160; x^3 y^3=(x y)(x^2+xy+x^2) ...

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Division of a Polynomial by a Polynomial

if x y + y ...

Question

if $\frac{x}{y} + \frac{y}{x} = - 1 (x, y \neq 0)$ then $x^{3} - y^{3}$

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Solution

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x y + y x = - 1 (x, y \neq 0)

x^{3} - y^{3}

\frac{x}{y} + \frac{y}{x} = - 1 (x, y \neq 0)

\frac{1}{2}

\frac{x}{y} + \frac{y}{x} = 1 (x, y \neq 0)

- \frac{1}{2}

\frac{x}{y} + \frac{y}{x} = - 1

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