Question

_{^{\(\log_3\dfrac{4x^2+2}{x^6+x^2+1}=x^6-3x^2-1\)}}

Answer 1

\(log_3^{4x^2+2}-log_3^{x^6+x^2+1}=x^6-3x^2-1\)

\(\Leftrightarrow log_3^{4x^2+2}+4x^2+2=log_3^{x^6+x^2+1}+x^6+x^2+1\)

Xét hàm \(f\left(t\right)=log_3^t+t\Rightarrow f'\left(t\right)=\dfrac{1}{tln\left(3\right)}+1>0\)

Vậy hs đb 

\(\Rightarrow f\left(4x^2+2\right)=f\left(x^6+x^2+1\right)\Rightarrow4x^2+2=x^6+x^2+1\)

\(\Leftrightarrow x^6-3x^2-1=0\)bn xứ lí nốt nhé ( đặt ẩn x^2 = t nhé )