3×4^х+2×9^х=5×6^х найти х

Question

3×4^х+2×9^х=5×6^х найти х

Answer 1

3×4^х+2×9^х=5×6^х

3×4^х+2×9^х- 5×6^х=0 /  9^х

3(4/9)ˣ +2 -5(6/9)ˣ =0

3(2/3)²ˣ -5(2/3)ˣ +2=0     (2/3)ˣ=a  a>0

3a²- 5a+2=0

D=25+24=1

a₁=(5+1)/6=1   (2/3)ˣ=1      x₁=0

a₂=(5-1)/6=2/3  (2/3)ˣ= 2/3  x₂=1