A 4919 Antoine Verroken
Q1. 1. Computer :
8^x - 18^x = 18^x - 27^x = - 19.0831…..
2. théorique :
(1) diviser par 27^x : (2/3)^(3*x) -2*(2/3)^x+1 =0 ou
X^3 – 2*X + 1 = 0 avec (2/3)^x = X ( X – 1 ) * ( X² + X – 1 ) = 0
X = ( sqrt(5)-1) / 2
x = ln(( sqrt(5)-1)/2)/ln(2/3) = 1.186814393
Q2. x² + 26455 = 2^y x = 1011 y = 20
2^20 = 1048576
Q3. x + 10 1° term x entier positif x + 4000 7° term
( x +10) * r^6 = x + 4000
r = (( 4000 + x ) / ( 10 + x )) ^ (1/6) = 3/2 x = 374 4° term 384 * (3/2)³ = 1296
