Đáp án:
`a) x=1; x=0 b) x=1; x=0`
`c) x=±1; x=0 d) x=±2; x=0`
`e) x=±3; x=0 f) x±2; x=0`
Giải thích các bước giải:
Bài 5:
`a) x^2=x`
`⇒x^2-x=0`
`x(x-1)=0`
`⇒`\(\left[ \begin{array}{l}x=0\\x-1=0\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x=1\end{array} \right.\)
Vậy `x=1; x=0`
`b) x^8=x`
`⇒x^8-x=0`
`x(x^7-1)=0`
`⇒`\(\left[ \begin{array}{l}x=0\\x^7-1=0\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x^7=1\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x^7=1^7\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x=1\end{array} \right.\)
Vậy `x=1; x=0`
`c) x^11=x`
`⇒x^11-x=0`
`x(x^10-1)=0`
`⇒`\(\left[ \begin{array}{l}x=0\\x^{10}-1=0\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x^{10}=1\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x^{10}=±1^{10}\end{array}\right.\)`⇒`\(\left[ \begin{array}{l}x=0\\x=±1\end{array} \right.\)
Vậy `x=±1; x=0`
`d) x^3=4x`
`⇒x^3-4x=0`
`x(x^2-4)=0`
`⇒`\(\left[ \begin{array}{l}x=0\\x^2-4=0\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x^2=4\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x^2=±2^2\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x=±2\end{array} \right.\)
Vậy `x=±2; x=0`
`e) x^3=9x`
`x^3-9x=0`
`x(x^2-9)=0`
`⇒`\(\left[ \begin{array}{l}x=0\\x^2-9=0\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x^2=9\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x^2=±3^2\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x=±3\end{array} \right.\)
Vậy `x=±3; x=0`
`f) x^5=16x`
`x^5-16x=0`
`x(x^4-16)=0`
`⇒`\(\left[ \begin{array}{l}x=0\\x^4-16=0\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x^4=16\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x^4=±2^4\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}x=0\\x=±2\end{array} \right.\)
Vậy `x=±2; x=0`
