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\(A=\frac{\sqrt{x}\left(\sqrt{x}+2\right)}{x-4}+\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}{x-4}+\frac{\sqrt{x}-10}{x-4}\)
\(A=\frac{x+2\sqrt{x}+x-3\sqrt{x}+2+\sqrt{x}-10}{x-4}\)
\(A=\frac{2x-8}{x-4}=\frac{2\left(x-4\right)}{x-4}=2\)
\(B=\left(13-4\sqrt{3}\right)\left(7+4\sqrt{3}\right)-8\sqrt{20+2\sqrt{\left(3\sqrt{3}+4\right)^2}}\)
\(B=43+24\sqrt{3}-8\sqrt{20+6\sqrt{3}+8}\)
\(B=43+24\sqrt{3}-8\sqrt{28+6\sqrt{3}}\)
\(B=43+24\sqrt{3}-8\sqrt{\left(3\sqrt{3}+1\right)^2}\)
\(B=43+24\sqrt{3}-24\sqrt{3}-8\)
\(B=35\)
b,\(\sqrt{16\left(x+1\right)}-\sqrt{9\left(x+1\right)}+\sqrt{4\left(x+1\right)}-16\sqrt{x+1}=0\) (dk \(x\ge-1\)
\(\Leftrightarrow\sqrt{x+1}\left(4-3+2-16\right)=0\)
\(\Leftrightarrow\sqrt{x+1}.-13=0\)
\(\Leftrightarrow x=-1\)
\(a,\sqrt{x^2-10x+2}=x-2\)
\(\Rightarrow x^2-10x+25=\left(x-2\right)^2\)
\(\Rightarrow x^2-10x+25=x^2-4x+4\)
\(\Rightarrow10x+25=4x+4\)
\(\Rightarrow10x-4x=4-25\)
\(\Rightarrow6x=-21\Leftrightarrow x=-\frac{21}{6}=-\frac{7}{2}\)
\(b,\sqrt{43-x}=x-1\)
\(\Rightarrow43-x=\left(x-1\right)^2\)
\(\Rightarrow43-x=x^2-2x+1\)
\(\Rightarrow42=x^2-3x\)
\(\Rightarrow42=x\left(x-3\right)\)
\(c,\sqrt{x-5}=4\)
\(\Rightarrow x-5=16\)
\(\Rightarrow x=16+5=21\)
a) \(\sqrt{x^2-10x+25}=x-2\)
\(\Leftrightarrow\sqrt{\left(x-5\right)^2}=x-2\)
\(\Leftrightarrow x-5=x-2\)
\(\Leftrightarrow x-x=-2+5\left(vonghiem\right)\)
a)\(\sqrt{x^2-10x+25}=x+2\)
\(\Leftrightarrow\sqrt{\left(x-5\right)^2}=x+2\)
\(\Leftrightarrow\left|x-5\right|=x+2\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=x+2\\x-5=-x-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-x=5+2\\x+x=5-2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}0x=7\\2x=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}0x=7\left(lo\text{ạ}i\right)\\x=\dfrac{3}{2}\left(nh\text{ậ}n\right)\end{matrix}\right.\)
vậy
\(b.\sqrt{43-x}=x-1\left(ĐK:43\ge x\ge1\right)\)
\(\Leftrightarrow43-x=x^2-2x+1\)
\(\Leftrightarrow43-x^2+x-1=0\)
\(\Leftrightarrow x^2-x-42=0\)
\(\Leftrightarrow x^2-7x+6x-42=0\)
\(\Leftrightarrow x\left(x-7\right)+6\left(x-7\right)=0\)
\(\Leftrightarrow\left(x-7\right)\left(x+6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=7\left(n\right)\\x=-6\left(l\right)\end{matrix}\right.\)
\(c.\sqrt{x-5}=4\left(ĐK:x\ge5\right)\)
\(\Leftrightarrow x-5=16\)
\(\Leftrightarrow x=21\left(n\right)\)