If $$x^{4} + x^{2} y^{2} + y^{4} = 273$$ and $$x^{2} - xy + y^{2} = 13$$, then the value of xy is :

$$x^{2} - xy + y^{2} = 13$$ ---(1)

$$\Rightarrow$$ $$x^{4} + x^{2} y^{2} + y^{4} = 273$$

$$\Rightarrow$$ $$(x^{2} + xy + y^{2})(x^{2} - xy + y^{2}) = 273$$ ---(2)

put the value of eq(1) in eq(2)-

$$(x^{2} + xy + y^{2})(13) = 273$$

$$\Rightarrow$$ $$(x^{2} + xy + y^{2}) = 21$$

$$\Rightarrow$$ $$(x^{2} + xy + y^{2} + xy - xy) = 21$$

$$\Rightarrow$$ $$(x^{2} - xy + y^{2} + 2xy) = 21$$

put the value from eq(1)

13 + 2xy = 21

$$\Rightarrow$$ 2xy = 8

$$\Rightarrow$$ xy = 4

$$\therefore$$ The value of xy is 4.