Câu hỏi của nguyễn viết hạ long

Question

Tính:$\sqrt{\frac{9}{\sqrt{14+4\sqrt{6}}}}-\sqrt{\frac{9}{\sqrt{14-4\sqrt{6}}}}$

%Hz@ · Accepted Answer

$\sqrt{\frac{9}{\sqrt{14+4\sqrt{6}}}}-\sqrt{\frac{9}{\sqrt{14-4\sqrt{6}}}}$$=\sqrt{\frac{9}{\sqrt{\left(\sqrt{12}\right)^2+2\cdot\sqrt{12}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}}}-\sqrt{\frac{9}{\sqrt{\left(\sqrt{12}\right)^2-2\cdot\sqrt{12}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}}}$$=\sqrt{\frac{9}{\sqrt{12}+\sqrt{2}}}-\sqrt{\frac{9}{\sqrt{12}-\sqrt{2}}}$$=\frac{3}{\sqrt{\sqrt{12}+\sqrt{2}}}-\frac{3}{\sqrt{\sqrt{12}-\sqrt{2}}}=\frac{3\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)-3\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)}{\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\sqrt{12-2}}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\sqrt{10}}$$=\frac{3\left(\sqrt{2\sqrt{3}-\sqrt{2}}-\sqrt{2\sqrt{3}+\sqrt{2}}\right)}{\sqrt{10}}$$=\frac{3}{\sqrt{10}}$Câu trả lời: $\sqrt{\frac{9}{\sqrt{14+4\sqrt{6}}}}-\sqrt{\frac{9}{\sqrt{14-4\sqrt{6}}}}$$=\sqrt{\frac{9}{\sqrt{\left(\sqrt{12}\right)^2+2\cdot\sqrt{12}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}}}-\sqrt{\frac{9}{\sqrt{\left(\sqrt{12}\right)^2-2\cdot\sqrt{12}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}}}$$=\sqrt{\frac{9}{\sqrt{12}+\sqrt{2}}}-\sqrt{\frac{9}{\sqrt{12}-\sqrt{2}}}$$=\frac{3}{\sqrt{\sqrt{12}+\sqrt{2}}}-\frac{3}{\sqrt{\sqrt{12}-\sqrt{2}}}=\frac{3\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)-3\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)}{\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\sqrt{12-2}}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\sqrt{10}}$$=\frac{3\left(\sqrt{2\sqrt{3}-\sqrt{2}}-\sqrt{2\sqrt{3}+\sqrt{2}}\right)}{\sqrt{10}}$$=\frac{3}{\sqrt{10}}$

Trần Tuyết Như · Answer

$\sqrt{\frac{9}{\sqrt{14+4\sqrt{6}}}}-\sqrt{\frac{9}{\sqrt{14-4\sqrt{6}}}}$$=\sqrt{\frac{9}{\sqrt{\left(\sqrt{12}\right)^2+2\cdot\sqrt{12}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}}}-\sqrt{\frac{9}{\sqrt{\left(\sqrt{12}\right)^2-2\cdot\sqrt{12}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}}}$$=\sqrt{\frac{9}{\sqrt{12}+\sqrt{2}}}-\sqrt{\frac{9}{\sqrt{12}-\sqrt{2}}}$$=\frac{3}{\sqrt{\sqrt{12}+\sqrt{2}}}-\frac{3}{\sqrt{\sqrt{12}-\sqrt{2}}}=\frac{3\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)-3\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)}{\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\sqrt{12-2}}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\sqrt{10}}$$=\frac{3\left(\sqrt{2\sqrt{3}-\sqrt{2}}-\sqrt{2\sqrt{3}+\sqrt{2}}\right)}{\sqrt{10}}$bí....!!!Câu trả lời: $\sqrt{\frac{9}{\sqrt{14+4\sqrt{6}}}}-\sqrt{\frac{9}{\sqrt{14-4\sqrt{6}}}}$$=\sqrt{\frac{9}{\sqrt{\left(\sqrt{12}\right)^2+2\cdot\sqrt{12}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}}}-\sqrt{\frac{9}{\sqrt{\left(\sqrt{12}\right)^2-2\cdot\sqrt{12}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}}}$$=\sqrt{\frac{9}{\sqrt{12}+\sqrt{2}}}-\sqrt{\frac{9}{\sqrt{12}-\sqrt{2}}}$$=\frac{3}{\sqrt{\sqrt{12}+\sqrt{2}}}-\frac{3}{\sqrt{\sqrt{12}-\sqrt{2}}}=\frac{3\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)-3\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)}{\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\sqrt{12-2}}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\sqrt{10}}$$=\frac{3\left(\sqrt{2\sqrt{3}-\sqrt{2}}-\sqrt{2\sqrt{3}+\sqrt{2}}\right)}{\sqrt{10}}$bí....!!!

Trí Tiên亗 · Answer

$\sqrt{\frac{9}{\sqrt{14+4\sqrt{6}}}}-\sqrt{\frac{9}{\sqrt{14-4\sqrt{6}}}}$$=\sqrt{\frac{9}{\sqrt{\left(\sqrt{12}\right)^2+2\cdot\sqrt{12}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}}}-\sqrt{\frac{9}{\sqrt{\left(\sqrt{12}\right)^2-2\cdot\sqrt{12}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}}}$$=\sqrt{\frac{9}{\sqrt{12}+\sqrt{2}}}-\sqrt{\frac{9}{\sqrt{12}-\sqrt{2}}}$$=\sqrt{\frac{9}{\sqrt{12}+\sqrt{2}}}-\sqrt{\frac{9}{\sqrt{12}-\sqrt{2}}}$$=\frac{3\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)-3\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)}{\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\sqrt{12-2}}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\sqrt{10}}$$=\frac{3\left(\sqrt{2\sqrt{3}-\sqrt{2}}-\sqrt{2\sqrt{3}+\sqrt{2}}\right)}{\sqrt{10}}$$=\frac{3.\left(-\sqrt{2\sqrt{3}-\sqrt{2}}\right)}{\sqrt{10}}$$=\frac{3}{\sqrt{10}}$Câu trả lời: $\sqrt{\frac{9}{\sqrt{14+4\sqrt{6}}}}-\sqrt{\frac{9}{\sqrt{14-4\sqrt{6}}}}$$=\sqrt{\frac{9}{\sqrt{\left(\sqrt{12}\right)^2+2\cdot\sqrt{12}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}}}-\sqrt{\frac{9}{\sqrt{\left(\sqrt{12}\right)^2-2\cdot\sqrt{12}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}}}$$=\sqrt{\frac{9}{\sqrt{12}+\sqrt{2}}}-\sqrt{\frac{9}{\sqrt{12}-\sqrt{2}}}$$=\sqrt{\frac{9}{\sqrt{12}+\sqrt{2}}}-\sqrt{\frac{9}{\sqrt{12}-\sqrt{2}}}$$=\frac{3\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)-3\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)}{\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\left(\sqrt{\sqrt{12}+\sqrt{2}}\right)\left(\sqrt{\sqrt{12}-\sqrt{2}}\right)}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\sqrt{12-2}}$$=\frac{3\sqrt{\sqrt{12}-\sqrt{2}}-3\sqrt{\sqrt{12}+\sqrt{2}}}{\sqrt{10}}$$=\frac{3\left(\sqrt{2\sqrt{3}-\sqrt{2}}-\sqrt{2\sqrt{3}+\sqrt{2}}\right)}{\sqrt{10}}$$=\frac{3.\left(-\sqrt{2\sqrt{3}-\sqrt{2}}\right)}{\sqrt{10}}$$=\frac{3}{\sqrt{10}}$

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