If $x^4+y^4+x^2 y^2=21$ and $x^2+y^2-x y=7$, then what is the value of $\frac{x}{y}+\frac{y}{x}$ ?

$-\frac{5}{2}$

x⁴ + x²y² + y⁴ = (x² – xy + y²) (x² + xy + y²)

If $x^4+y^4+x^2 y^2=21$

$x^2+y^2-x y=7$

Then, $x^2+y^2+x y$ = \(\frac{21}{7}\) = 3

what is the value of $\frac{x}{y}+\frac{y}{x}$ = \(\frac{x^2 + y^2}{xy}\)---(A)

$x^2+y^2-x y=7$

 $x^2+y^2+x y$ = 3

So from these two equations ,

x² + y² = 5

xy = -2

Put in (A)

\(\frac{x^2 + y^2}{xy}\) = -\(\frac{5}{2}\)