Chứng minh

T

trinhminh18

Ta có:
$(5+2\sqrt{6})(49-20\sqrt{6})\sqrt{5-2\sqrt{6}}=(5+2\sqrt{6})(5-2\sqrt{6})^2\sqrt{5-2\sqrt{6}}= (\sqrt{5-2\sqrt{6}})^3$
$= (\sqrt{(\sqrt{3}-\sqrt{2})^2})^3 = (\sqrt{3}-\sqrt{2})^3 = 3\sqrt{3}-9\sqrt{2} + 6\sqrt{3} -2\sqrt{2} = 9\sqrt{3}-11\sqrt{2}$
\Rightarrow$\dfrac{(5+2\sqrt{6})(49-20\sqrt{6})\sqrt{5-2\sqrt{6}}}{9\sqrt{3}}= \dfrac{ 9\sqrt{3}-11\sqrt{2}}{9\sqrt{3}}= 1- \dfrac{11\sqrt{2}}{9\sqrt{3}}$
\Rightarrow cần c/m $ 1- \dfrac{11\sqrt{2}}{9\sqrt{3}} -11\sqrt{2}=1$ (vô lí)
\Rightarrow sai đề
 
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