Question

if X divided by y + y divided by x is equal to -1 their x or y is not equal to zero then the value of x cube minus y cube is

Answer 1

Step-by-step explanation:

x/y + y/x =-1.

x^2 +Y^2 +xy=0. ......(1).

find here x^3 -y^3=?

We know that ...

x^3 -y^3= (x-y)(x^2 +y^2 +xy)

. =(x -y)(0). 4

[ put value by (1).]

so ..

x^3 -y^3=0

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Answer 2

Answer:

$\blue{{x}^{3} - {y}^{3} = 0}$

Step-by-step explanation:

Given that

$\frac{x}{y} + \frac{y}{x} = - 1 \: \: \: x \: ,\: y \neq \: 0$

To find

${x}^{3} - {y}^{3}$

we know that

$\boxed{ \bold{ \green{{x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) }}}$

So,from given condition find the values of RHS of expression

Take LCM

$\frac{ {x}^{2} + {y}^{2} }{xy} = - 1 \\ \\ cross \: multiply \\ \\ {x}^{2} + {y}^{2} = - xy \\ \\ {x}^{2} + xy + {y}^{2} = 0$

place the value

${x}^{3} - {y}^{3} = (x - y)( 0 ) \\ \\{x}^{3} - {y}^{3} = 0$

This is the only answer;if data provided is correct.

Hope it helps you.