Question

Pt log₃(x³+2x)=1 có nghiệm là

A.x=1;x=-3 B.x=1 Cx=-1x=3

Answer 1

đk:x >0

Pt\(\Leftrightarrow\) X³ +2X =3

\(\Leftrightarrow\)X=1 (thoả mãn)

chọn A

Answer 2

\(\log_3(x^3+2x)=1\\\leftrightarrow x^3+2x=3\\\leftrightarrow x^3+2x-3=0\\\leftrightarrow x^3-x^2+3x+x^2-x+3=0\\\leftrightarrow x(x^2-x+3)+(x^2-x+3)=0\\\leftrightarrow (x+1)(x^2-x+3)=0\\\leftrightarrow x+1=0\quad or\quad x^2-x+3=0\\\leftrightarrow x=-1\quad or\quad \bigg(x-\dfrac{1}{2}\bigg)^2+\dfrac{11}{4}=0(\rm vô\,\, lý)\\\leftrightarrow x=-1\\\to C\)