Question

sa se rezolve ecuatia:
f] 3*9^x+2*12^x=16^x

Answer 1

Răspuns:

3*9ˣ+2*12ˣ=16ˣ

2*(3²ˣ)+2*3ˣ*4ˣ=4²ˣ

Impari egalitatea prin 3²ˣ

2(3²ˣ/3²ˣ)+2(3ˣ/3ˣ)*(4ˣ/3x)=4²ˣ/3²ˣ

2*1+2*1*(4/3)ˣ=(4/3)²ˣ

2+2*(4/3)ˣ=(4/3)²ˣ

Substitutie

(4/3)ˣ =y    y>0

2+2y=y²

y²-2y-2=0

Δ=4+8=12

y1=(2-√12)/2=(2-2√3)/2=1-√3<0  Nu convine  ecuatiei

y2=1+√3 >0 se accepta

2/3ˣ=1+$\sqrt{3}$

x=log(2/3)(1+√3)

Explicație pas cu pas:

x=