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Algebra Difficulty 4.6 AIME Find the answer
x,y are positive real numbers such that x+y2=xy. What is the smallest possible value of x?
A number or a short expression. Spacing and $ signs are ignored.
Solution
4 Notice that x=y2/(y−1)=2+(y−1)+1/(y−1)≥2+2=4. Conversely, x=4 is achievable, by taking y=2.
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