2 câu trả lời
`#tnvt`
`\sqrt{6-\sqrt{11}}-\sqrt{6+\sqrt{11}}`
`=\frac{\sqrt{2}.(\sqrt{6-\sqrt{11}}-\sqrt{6+\sqrt{11}})}{\sqrt{2}}`
`=\frac{\sqrt{12-2\sqrt{11}}-\sqrt{12+2\sqrt{11}}}{\sqrt{2}}`
`=\frac{\sqrt{11-2\sqrt{11}+1}-\sqrt{11+2\sqrt{11}+1}}{\sqrt{2}}`
`=\frac{\sqrt{(\sqrt{11}-1)^2}-\sqrt{(\sqrt{11}+1)^2}}{\sqrt{2}}`
`=\frac{|\sqrt{11}-1|-|\sqrt{11}+1|}{\sqrt{2}}`
`=\frac{\sqrt{11}-1-\sqrt{11}-1}{\sqrt{2}}`
`=-2/(\sqrt{2})`
`=-\sqrt{2}`
Đáp án+Giải thích các bước giải:
`\sqrt{6-\sqrt{11}}-\sqrt{6+\sqrt{11}}`
`=\sqrt{\frac{12-2\sqrt{11}}{2}}-\sqrt{\frac{12+2\sqrt{11}}{2}}`
`=\sqrt{\frac{11-2.\sqrt{11}.1+1}{2}}-\sqrt{\frac{11+2.\sqrt{11}.1+1}{2}}`
`=\sqrt{\frac{(\sqrt{11}-1)^2}{2}}-\sqrt{\frac{(\sqrt{11}+1)^2}{2}}`
`=\frac{|\sqrt{11}-1|}{\sqrt{2}}-\frac{|\sqrt{11}+1|}{\sqrt{2}}`
`=\frac{|\sqrt{11}-1|-|\sqrt{11}+1|}{\sqrt{2}}`
`=\frac{\sqrt{11}-1-\sqrt{11}-1}{\sqrt{2}}`
`=\frac{-2}{\sqrt{2}}`
`=-\sqrt{2}`