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Bài 1 : Thực hiện phép tính :
a ) \(\sqrt{9-2\sqrt{20}}+\sqrt{12-2\sqrt{35}}\)
\(=\sqrt{5-2\sqrt{20}+4}+\sqrt{7-2\sqrt{35}+5}\)
\(=\sqrt{\left(\sqrt{5}-2\right)^2}+\sqrt{\left(\sqrt{7}-\sqrt{5}\right)}^2\)
\(=\sqrt{5}-2+\sqrt{7}-\sqrt{5}\)
\(=\sqrt{7}-2\)
b ) \(\sqrt{5-\sqrt{21}}-\sqrt{5+\sqrt{21}}\)
\(=\sqrt{\dfrac{2\left(5-\sqrt{21}\right)}{2}}-\sqrt{\dfrac{2\left(5+\sqrt{21}\right)}{2}}\)
\(=\sqrt{\dfrac{10-2\sqrt{21}}{2}}-\sqrt{\dfrac{10+2\sqrt{21}}{2}}\)
\(=\dfrac{\sqrt{7-2\sqrt{21}+3}}{\sqrt{2}}-\dfrac{\sqrt{7+2\sqrt{21}+3}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}}{\sqrt{2}}-\dfrac{\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{7}-\sqrt{3}}{\sqrt{2}}-\dfrac{\sqrt{7}+\sqrt{3}}{\sqrt{2}}\)
\(=\dfrac{-2\sqrt{3}}{\sqrt{2}}=-\sqrt{6}\)
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a. =\(\frac{x\sqrt{xy}+y\sqrt{x^2}-x\sqrt{y^2}-y\sqrt{xy}}{\sqrt{xy}}\)=\(\frac{x\sqrt{xy}+xy-xy-y\sqrt{xy}}{\sqrt{xy}}\)
=\(\frac{x\sqrt{xy}-y\sqrt{xy}}{\sqrt{xy}}\)=\(\frac{\sqrt{xy}\left(x-y\right)}{\sqrt{xy}}\)=\(x-y\)
b. =\(\frac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x-1}}\)=\(x+\sqrt{x}+1\)
1/ Thực hiện phép tính
a) √9−2√20+√12−2√35
\(=\sqrt{\left(\sqrt{5}-\sqrt{4}\right)^2}+\sqrt{\left(\sqrt{7}-\sqrt{5}\right)^2}\)
\(=\sqrt{5}-\sqrt{4}+\sqrt{7}-\sqrt{5}=\sqrt{7}-\sqrt{4}=\sqrt{7}-2\)