Question

9^x +3^x -12=0 cum rezolv

Answer 1

9^x+3^x=12 notam 3^x cu a
3^2^x+3^x=12
a^2+a-12=0 aceasta e o ec de gr 2 deci


delta=1-4×1×-12=1+48=49
a=-1+,-radical din delta/2
a=-1+7/2
a=3
a=-1-7/2
a=-4

3^x nu poate fi -4 deci 3^x=3 deci x=1

Answer 2

[tex] 9^{x} +3^{x}-12=0 \\\\{(3^{x})^{2}+3^{x}-12=0 \\\\[/tex]

Δ=1-4*(-12)
Δ=49
      ↓

[tex] 3^{x_{1} } = \frac{-1+7}{2} =3\\\\ 3^{x_{2} } = \frac{-1-7}{2} =-4 [/tex]

cum 3ˣ ∈ R => 3ˣ=3 => x=1 - singura solutie in R