Introduction to Substitute Rearrange Factor The Quartic Four Roots Fall Out Math Olympiad
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Substitute Rearrange Factor The Quartic Four Roots Fall Out Math Olympiad Comprehensive Overview
(x²+54x+9)/(x+3)=14√x → Find all values of x Let t=√x so x=t². x⁴+3x³+6x+ x⁵-49=(x+1)(49x-1) → Find all real x. No
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Summary & Highlights for Substitute Rearrange Factor The Quartic Four Roots Fall Out Math Olympiad
- Cross multiplication,
- 4x⁴-8x³+4x-1=0 → Find all x. No
- (x²-2)²=x+2 → Find all real x Let y=x²-2. The equation becomes y²=x+2. Now write both equations side by side: y²-x=2 and x²-y=2.
- (x+2)⁵/[(x+1)⁵+(x+3)⁵]=3 → Find all values of x Let y=x+2. Then x+1=y-1 and x+3=y+1. Denominator: (y-1)⁵+(y+1)⁵. Expand ...
- x⁵+(6-x)⁵=1056 → Find all
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