Câu hỏi của Nguyễn Hải An

Question

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Vũ Đỗ Anh Thư · Accepted Answer

c)$\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}$

=$\dfrac{\sqrt{8-2\sqrt{7}}}{\sqrt{2}}-\dfrac{\sqrt{8+2\sqrt{7}}}{\sqrt{2}}$

=$\dfrac{\sqrt{\left(\sqrt{7}-1\right)^2}}{\sqrt{2}}-\dfrac{\sqrt{\left(\sqrt{7}+1\right)^2}}{\sqrt{2}}$

=$\dfrac{\left|\sqrt{7}-1\right|-\left|\sqrt{7}+1\right|}{\sqrt{2}}$

=$\dfrac{\sqrt{7}-1-\sqrt{7}-1}{\sqrt{2}}$

=$\dfrac{-2}{\sqrt{2}}$

=$-\sqrt{2}$

Câu trả lời:

c)$\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}$

=$\dfrac{\sqrt{8-2\sqrt{7}}}{\sqrt{2}}-\dfrac{\sqrt{8+2\sqrt{7}}}{\sqrt{2}}$

=$\dfrac{\sqrt{\left(\sqrt{7}-1\right)^2}}{\sqrt{2}}-\dfrac{\sqrt{\left(\sqrt{7}+1\right)^2}}{\sqrt{2}}$

=$\dfrac{\left|\sqrt{7}-1\right|-\left|\sqrt{7}+1\right|}{\sqrt{2}}$

=$\dfrac{\sqrt{7}-1-\sqrt{7}-1}{\sqrt{2}}$

=$\dfrac{-2}{\sqrt{2}}$

=$-\sqrt{2}$