A Nice Exponential Algebra Equation | Math Olympiad

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[@user-il4hm4yi4p]

Функция симметрична относительно х=-1.5. Замена t=x+1.5 приводит к биквадратному уравнению. Дальше дело техники

[@nalim81]

The root x=0 can be guessed immediately knowing that 2^4=16. After that, another root x=-3 can also be guessed from the symmetry of equation (i.e. looking for x where x+2=-1and x+1=-2 - same values under ^4, but swapped and with opposite sign). Expanding the equation, dividing it by 2x and then by x+3 gives x(x+1)(x^2+3x+6)=0. After that, checking that there are no more real roots or finding the remaining complex roots becomes trivial.

[@dardoburgos3179]

No entiendo nada.

[@comdo777]

asnwer=13x

[@user-nd7th3hy4l]

X=0 puis il faut rechercher.

[@roger7341]

Substitute x=y-3/2 for faster solution: (y+1/2)^4+(y-1/2)^4-17=2[y^4+6(1/2)^2y^2+(1/2)^4]-17=0
Rearrange to 16y^4+24y^2-135=0 yields y^2=(-24±96)/32=-15/4 or 9/4 and y=±i√15/2 or ±3/2
This gives x=y-3/2=±i√15/2-3/2 or 0 or -3