Question

[Dog Dog]

Bài1 thôi nhé🙏🙏🙏

Answer 1

[Nhan Thanh]

Bài 1:

1. ĐKXĐ: \(x\ge0\) 
\(x-7\sqrt{x}+10=0\)

\(\Leftrightarrow x-2\sqrt{x}-5\sqrt{x}+10=0\)

\(\Leftrightarrow\sqrt{x}\left(\sqrt{x}-2\right)-5\left(\sqrt{x}-2\right)=0\)

\(\Leftrightarrow\left(\sqrt{x}-2\right)\left(\sqrt{x}-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}-2=0\\\sqrt{x}-5=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=2\\\sqrt{x}=5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=25\end{matrix}\right.\) ( thỏa mãn đk )

Vậy \(S=\left\{4;25\right\}\)

2. ĐKXĐ: \(x\ge4\) 
\(\sqrt{x^2-16}-5\sqrt{x-4}=0\)

\(\Leftrightarrow\sqrt{x^2-16}=5\sqrt{x-4}\)

\(\Leftrightarrow x^2-16=25\left(x-4\right)\)

\(\Leftrightarrow x+4=25\)

\(\Leftrightarrow x=21\) ( thỏa mãn đk )

Vậy \(S=\left\{21\right\}\)

3. ĐKXĐ: \(x\ge-4\)
\(\sqrt{x^2-16}-3\sqrt{x+4}=0\)

\(\Leftrightarrow\sqrt{x^2-16}=3\sqrt{x+4}\)

\(\Leftrightarrow x^2-16=9\left(x+4\right)\)

\(\Leftrightarrow x-4=9\)

\(\Leftrightarrow x=13\) ( thỏa mãn đk )

Vậy \(S=\left\{13\right\}\)

Answer 2

[ILoveMath]

Bài 1:
a) ĐKXĐ: \(x\ge0\)

\(x-7\sqrt{x}+10=0\)

\(\Rightarrow x+10=7\sqrt{x}\)

\(\Rightarrow x^2+20x+100=49x\)

\(\Rightarrow x^2-29x+100=0\)

\(\Rightarrow\left(x^2-4x\right)-\left(25x-100\right)=0\)

\(\Rightarrow\left(x-4\right)\left(x-25\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-4=0\\x-25=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4\\x=25\end{matrix}\right.\)

b) ĐKXĐ:\(\left\{{}\begin{matrix}x^2-16\ge0\\x-4\ge0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\left(x-4\right)\left(x+4\right)\ge0\\x-4\ge0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x+4\ge0\\x-4\ge0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ge-4\\x\ge4\end{matrix}\right.\Rightarrow x\ge4\)

\(\sqrt{x^2-16}-5\sqrt{x-4}=0\)

\(\Rightarrow\sqrt{\left(x-4\right)\left(x+4\right)}-5\sqrt{x-4}=0\\ \Rightarrow\sqrt{x-4}\left(\sqrt{x+4}-5\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}\sqrt{x-4}=0\\\sqrt{x+4}-5=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x-4=0\\\sqrt{x+4}=5\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4\\x+4=25\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=4\\x=21\end{matrix}\right.\)