Question

x+y=10 and xy=5 the value of x/y+y/x=?

Answer 1

Answer:

$\frac{x}{y} + \frac{y}{x} \\ = \frac{x {}^{2} + y {}^{2} }{xy} \\ = \frac{(x + y) {}^{2} - 2xy}{xy} \\ = \frac{10 {}^{2} - 2 \times 5}{5} \\ = \frac{90}{5} \\ = 18$

Answer 2

We see that $\frac{x}{y}=\frac{x^2}{xy}$ and $\frac{y}{x}=\frac{y^2}{xy}$. Adding, we get $\frac{x^2+y^2}{xy}$. $(x+y)^2=x^2+2xy+y^2=x^2+y^2+10 \implies x^2+y^2 = 90$. Thus, the answer is $\frac{90}{5}=\boxed{18}$.