\(\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)\sqrt{6-2\sqrt{5}}=8\)

\(\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)^2=8\)

\(\left(3+\sqrt{5}\right)\left(6-2\sqrt{5}\right)=8\)

\(18-6\sqrt{5}+6\sqrt{5}-10=8\)

8=8 ( luôn đúng )

\(C=\frac{\sqrt{x+3}}{\sqrt{x-2}}\)\(đkxđ\Leftrightarrow\hept{\begin{cases}x-2\ge0\\x-2\ne0\end{cases}}\)

\(\Rightarrow x-2>0\Rightarrow x>2\)

\(D=\frac{2\sqrt{x}-1}{\sqrt{x}+3}\)\(đkxđ\Leftrightarrow\hept{\begin{cases}x\ge0\\\sqrt{x}+3\ne0\left(tm\right)\end{cases}}\)

\(\Rightarrow x\ge0\)

\(\sqrt{ab}-\sqrt{a}-\sqrt{b}+1\)

\(=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)\)

\(=\left(\sqrt{a}-1\right)\left(\sqrt{b}-1\right)\)

\(\sqrt{ab}-\sqrt{a}-\sqrt{b}+1=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)=\left(\sqrt{a}-1\right)\left(\sqrt{b}-1\right)\)

\(=\sqrt{a}\left(\sqrt{a}+1\right)+2\sqrt{b}\left(\sqrt{a}+1\right)=\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\sqrt{b}\right)\)

=(x^8-x^7+x^6)-(x^6-x^5+x^4)-(x^3-x^2+x)+(x^2-x+1)

=x^6(x^2-x+1)-x^4(x^2-x+1)-x(x^2-x+1)+(X^2-x+1)

=(x^6-x^4-x+1)(x^2-x+1)>0(vì x^6-x^4-x+1>0 và x^2-x+1>0)

=19.94427191 (haha)