Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.6 AIME Find the answer

The graph of $x^{4}=x^{2} y^{2}$ is a union of $n$ different lines. What is the value of $n$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

The equation $x^{4}-x^{2} y^{2}=0$ factors as $x^{2}(x+y)(x-y)=0$ , so its graph is the union of the three lines $x=0, x+y=0$ , and $x-y=0$ .

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