Question

Rezolvaţi ecuaţia 10^x + 4^x - 2*25^x = 0

Answer 1

fie 5^x=u si 2^x=v
uv+v²-2u²=0
impartim prin v²≠0, ptca v este o exponentiala

u/v +1-2 (u/v)²=0
fie u/v=w

-2w²+w+1=0
2w²-w-1=0
w1,2= (1+-√(1+8))/4
w>0 ptca e exponentiala
w2=(1+3)/4=1
 (5/2)^x=1
x=0
verificare
1+1-2=0 adevarat