Đề như sau:
View attachment 11961
xin hãy giúp mình =)
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$F=\dfrac{(x+\sqrt{5})(\sqrt{x}-\sqrt{x-\sqrt{5}})}{x-x-\sqrt{5}}+\dfrac{(x-\sqrt{5})(\sqrt{x}+\sqrt{x-\sqrt{5}})}{x-x+\sqrt{5}}$
$F=\dfrac{x(\sqrt{x+\sqrt{5}}+\sqrt{x-\sqrt{5}})-2\sqrt{5x}+\sqrt{5}(\sqrt{x+5}-\sqrt{x-\sqrt{5}})}{\sqrt{5}}$
Ta có:
$\sqrt{10}F(3)=3(\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}})-2\sqrt{30}+\sqrt{5}(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}})$
$\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}=2\sqrt{5}$
$\sqrt{6+\sqrt{5}}-\sqrt{6-2\sqrt{5}}=2$
$\sqrt{10}F(3)=8\sqrt{5}-2\sqrt{30}$
$F(3)=4\sqrt{2}-2\sqrt{3}$
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