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If x/y + y/x=-1( where x,y …

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If x/y + y/x=-1( where x,y is not equal to 0) then find the value of xcube - ycube

Posted by Bhabana Sarma 4 years, 2 months ago

Gaurav Seth 4 years, 2 months ago

We know that,x³ - y³ = (x - y)(x² + xy + y²) ....(i)

Given that, x/y + y/x = -1
(x² + y²)/xy = -1
x² + y² = -xy
x² + y² + xy = 0
(x² + xy + y²) = 0

Multyplying by (x - y) on both sides we get,(x - y)(x² + xy + y²) = (x - y) × 0

x³ - y³ = 0 using (i)

ANSWER

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