How to solve this polynomial?

Question

How to get the solution for this polynomial? If $x/y + y/x = -1$ where $x$ and $y$ are not equal to zero, then what would be the value of $x^3 -y^3$

Note that there are no real $x,y$ such that $\frac{x}{y}+\frac{y}{x}=-1$. — André Nicolas, Jun 06 '13 at 15:48

score 4 · Accepted Answer · answered Jun 06 '13 at 15:29

4

Hint: $x^3 - y^3 = (x - y)(x^2 + y^2 + xy)$. Factor out $xy$ from the second term.

answered Jun 06 '13 at 15:29

Caleb Stanford

score 1 · Answer 2 · edited Jun 06 '13 at 17:49

1

Fint :we have $1+z+z^2+\dots+z^n=\frac{z^{n+1}-1}{z-1}$ and assume $z=\frac{x}{y}$ then $z+\frac1z=-1\to z^2+z+1=0\to \frac{z^3-1}{z-1}=0$

edited Jun 06 '13 at 17:49

Michael Hardy

answered Jun 06 '13 at 15:42

M.H

$\Large\color{blue}{+1}{nice work}$$\Large\color{blue}{❀}$ @Maisam Hedyelloo – Software Jun 06 '13 at 18:20
@faranak50:thx faranak – M.H Jun 06 '13 at 19:41

score 1 · Answer 3 · answered Jun 06 '13 at 15:46

1

$\frac{x}{y} + \frac y x = -1\\x^2+y^2=-xy\tag{multiply both sides by xy}\\x+y+xy=0$ Take the hint above to complete your working.

answered Jun 06 '13 at 15:46

bryan.blackbee

3 Answers3