A nice Math Olympiad Diophantine Algebra Equation Simplification |

Solve diophantine algebra equation #diophantine #olympiad
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[@himo3485]

40=(7+3)(7-3)=7^2-3^2 √7^√m=7^2 √3^√m=3^2 7^√m/2=7^2 3^√m/2=3^2 √m/2=2 √m=4 m=16

[@walterwen2975]

A nice Math Olympiad Diophantine Algebra Equation Simplification: (√7)^√m - (√3)^√m = 40; m = ? (√7)^√m > 40 > (√3)^√m; (√7)^√m - (√3)^√m = 40 = 49 - 9 = 7^2 - 3^2 = 7^(4/2) - 3^(4/2) = (√7)^4 - (√3)^4 = (√7)^√16 - (√3)^√16; m =16 Answer check: (√7)^√m - (√3)^√m = 40; Confirmed as shown Final answer: m = 16