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Câu hỏi: Phương trình $\log _{2}^{2}x-\left( 10+\log x \right){{\log }_{2}}x+\log {{x}^{10}}=0$ có tổng các nghiệm là A thì
A. $\sqrt{A}=11\sqrt{2}.$
B. $\sqrt{A}=5\sqrt{41}.$
C. $\sqrt{A}=3\sqrt{102}.$
D. $\sqrt{A}=10\sqrt{11}.$
A. $\sqrt{A}=11\sqrt{2}.$
B. $\sqrt{A}=5\sqrt{41}.$
C. $\sqrt{A}=3\sqrt{102}.$
D. $\sqrt{A}=10\sqrt{11}.$
Điều kiện: x > 0. Ta có
$\log _{2}^{2}x-\left( 10+\log x \right){{\log }_{2}}x+\log {{x}^{10}}=0\Leftrightarrow \log _{2}^{2}x-10{{\log }_{2}}x-\log x{{\log }_{2}}x+10\log x=0$
$\Leftrightarrow \left( \log x-{{\log }_{2}}x \right)\left( 10-{{\log }_{2}}x \right)=0\Leftrightarrow \left[ \begin{aligned}
& {{\log }_{2}}x=10 \\
& {{\log }_{2}}x=\log x \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& x={{2}^{10}} \\
& x=1 \\
\end{aligned} \right.$
$\Rightarrow A={{2}^{10}}+1=1025\Rightarrow \sqrt{A}=5\sqrt{41}.$
$\log _{2}^{2}x-\left( 10+\log x \right){{\log }_{2}}x+\log {{x}^{10}}=0\Leftrightarrow \log _{2}^{2}x-10{{\log }_{2}}x-\log x{{\log }_{2}}x+10\log x=0$
$\Leftrightarrow \left( \log x-{{\log }_{2}}x \right)\left( 10-{{\log }_{2}}x \right)=0\Leftrightarrow \left[ \begin{aligned}
& {{\log }_{2}}x=10 \\
& {{\log }_{2}}x=\log x \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& x={{2}^{10}} \\
& x=1 \\
\end{aligned} \right.$
$\Rightarrow A={{2}^{10}}+1=1025\Rightarrow \sqrt{A}=5\sqrt{41}.$
Đáp án B.