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\(5+\sqrt{5}=\sqrt{5}\left(\sqrt{5}+1\right)\)
\(3+\sqrt{3}=\sqrt{3}\left(\sqrt{3}+1\right)\)
\(\sqrt{14}+\sqrt{7}=\sqrt{7}\left(\sqrt{2}+1\right)\)
\(\sqrt{15}-\sqrt{6}=\sqrt{3}\left(\sqrt{5}-\sqrt{2}\right)\)
\(7-\sqrt{7}=\sqrt{7}\left(\sqrt{7}-1\right)\)
\(10-2\sqrt{10}=\sqrt{10}\left(\sqrt{10}-2\right)=\sqrt{20}\left(\sqrt{5}-\sqrt{2}\right)\)
\(4-4\sqrt{5}=4\left(1-\sqrt{5}\right)\)
\(5-2\sqrt{5}=\sqrt{5}.\left(\sqrt{5}-2\right)\)
\(5+\sqrt{5}=\sqrt{5}(\sqrt{5}+1)\)
\(3+\sqrt{3}=\sqrt{3}(\sqrt{3}+1)\)
\(\sqrt{14}+\sqrt{7}=\sqrt{7}(\sqrt{2}+1)\)
\(\sqrt{15}-\sqrt{6}=\sqrt{3}(\sqrt{5}-\sqrt{2})\)
\(7-\sqrt{7}=\sqrt{7}(\sqrt{7}+1)\)
\(10-2\sqrt{10}=\sqrt{10}(\sqrt{10}-2)=\sqrt{10}.\sqrt{2}(\sqrt{5}-\sqrt{2})=2\sqrt{5}(\sqrt{5}-\sqrt{2})\)
\(4-4\sqrt{5}=4(1-\sqrt{5})\)
\(5-2\sqrt{5}=\sqrt{5}(\sqrt{5}-2)\)
a: \(=\left(-\sqrt{5}-\sqrt{7}\right)\cdot\left(\sqrt{7}-\sqrt{5}\right)\)
\(=-\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}-\sqrt{5}\right)\)
=-2
b: \(=\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\)
\(=\dfrac{\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{3}-1+\sqrt{3}+1}{\sqrt{2}}=\sqrt{6}\)
c: \(=\dfrac{\sqrt{10}\left(\sqrt{2}-\sqrt{5}\right)}{\sqrt{2}-\sqrt{5}}-2-\sqrt{10}+3\sqrt{7}+2\)
\(=\sqrt{10}-\sqrt{10}+3\sqrt{7}=3\sqrt{7}\)
81 ; 11660 ; 2 ; 4 ; 6 ; 8 ; 10 ; 12 ; 14 ; 16 ; 18 ; 20 ; 34 ; 42 .
a,3x-6\(\sqrt{x}\)-6
=2(x-3\(\sqrt{x}\)-3)
=2(x-2\(\sqrt{x}\).\(\frac{3}{2}\)+\(\frac{9}{4}\)-\(\frac{21}{4}\))
=2[(x-\(\frac{3}{2}\))2-\(\frac{21}{4}\)]
2(x-\(\frac{3+\sqrt{21}}{2}\))(x-\(\frac{3-\sqrt{21}}{2}\))
b,x+4\(\sqrt{x}\)+3
=x+3\(\sqrt{x}\)+\(\sqrt{x}\)+3
=\(\sqrt{x}\)(\(\sqrt{x}\)+3) +(\(\sqrt{x}\)+3)
=(\(\sqrt{x}\)+1)(\(\sqrt{x}\)+3)
c,x-5\(\sqrt{x}\)-6
=x-6\(\sqrt{x}\)+\(\sqrt{x}\)-6
=\(\sqrt{x}\)(\(\sqrt{x}\)-6)+(\(\sqrt{x}\)-6)
=(\(\sqrt{x}\)+1)(\(\sqrt{x}\)-6)
d,x+5\(\sqrt{x}\)-14
=x+7\(\sqrt{x}\)-2\(\sqrt{x}\)-14
=\(\sqrt{x}\)(\(\sqrt{x}\)+7)-2(\(\sqrt{x}\)+7)
=(\(\sqrt{x}\)-2)(\(\sqrt{x}\)+7)