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Math Olympiad Math Olympiad [x/(x-1)]²+[x/(x+1)]²=10/9 → Find all values of x Let a=x/(x-1) and b=x/(x+1). Then a²+b²=10/9. Compute a+b and ab: a+b=2x²/(x²-1).
(x-1/2)³-(x-1/2)²+x=105/2 → Find x Let y=x-1/2. Then x=y+1/2. Substitute: y³-y²+(y+1/2)=105/2. y³-y²+y+1/2=105/2. y³-y²+y=52.
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- Difference of squares, substitution strategy,
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