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

2ˣnotam t.t>0

t²-3t+2=0

Δ=9-8=1

t₁=(3+1)/2=2

t₂=(3-1)/2=1

pt.t₁=2=>2ˣ=2=>injectivitatea functiei exponentiale x₁=1

pt.t₂=1=>2ˣ=1=>injectivitatea functiei exponentiale x₂=0

S={0;1}