Question 16

$$x$$ and $$y$$ are positive integers. If $$x^4 + y^4 + x^2y^2 = 481$$ and $$xy = 12$$, then what is the value of $$x^2 - xy + y^2$$?

Solution

$$x^4+y^4+x^2y^2=481$$

or, $$\left(x^2\right)^2+\left(y^2\right)^2+2x^2y^2-x^2y^2=481\ .$$

or, $$\left(x^2+y^2\right)^2=481+144=25^2\ \left(given\ xy=12\right)\ .$$

or, $$\left(x^2+y^2\right)=25\ .$$

So, $$x^2-xy+y^2=25-12=13.$$

B is correct choice.

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