Question

If x by y + y by x is equal to minus 1 find x cube minus y cube

Answer 1

$\frac{x}{y} + \frac{y}{x} = - 1 \\ \frac{( {x }^{2} - {y}^{2} )}{xy} = - 1 \\ {x}^{2} - {y}^{2} = - xy \\ ( {x}^{2} + xy - {y}^{2} )= 0 \\ then \: we \: know \: \\ {x}^{3} - {y}^{3} \\ = (x - y)( {x}^{2} + xy - {y}^{2} ) \\ = (x - y) \times 0 \\ = 0$
x³-y³= 0
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