Question

Sa se determine solutiile reale ale ecuatiei 4^x-3•2^x+2=0

Answer 1

4ˣ-3*2ˣ+2=0<=>2²ˣ-3*2ˣ+2=0

Notam t=2ˣ;t>0

t²-3t+2=0

Δ=9-8=1

t₁=(3-1)/2=2/2=1

t₂=(3+1)/2=4/2=2

pt.t₁=1=>2ˣ=1=>x₁=0

pt.t₂=2=>2ˣ=2=>x₂=1

S={0,1}