Question

x/y + y/x = -1(x,y not equal to 0),then,the value of x^3-y^3 is?

Answer 1

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

Answer 2

multiplying equation with xy we get. . .
x^2+y^2=-xy
x^2+y^2+xy=0
multiplying with (x-y) on both sides
we get x^3+xy^2+x^2y-y^3-xy^2-x^y=0
that is x^3-y^3=0

Answer 3

x^2+y^2+xy = 0 ??? how???????

Answer 4

x^2+y^2=-xy
x^2+y^2+xy=0 (taking -xy to left hand side

Answer 5

\[\frac{x}{y} + \frac{y}{x} = -1 \implies \frac{x^2 + y^2}{xy} = -1 \implies x^2 + y^2 = -xy\]

Add xy both sides:

\[x^2 + y^2 + xy = 0\]


Now use:

\[\large x^3 - y^3 = (x-y)(x^2 + y^2 +xy) \implies \color{blue}{(x-y)(0)}\]

multiply them you will have your answer..

Answer 6

now i ge it thanks

Answer 7

Welcome dear..