rút gọn biểu thức B=(√2+1)(√3+1)(√6+1)(5-2√2-√3)
1 câu trả lời
`#huy`
`B=(\sqrt{2}+1)(\sqrt{3}+1)(\sqrt{6}+1)(5-2\sqrt{2}-\sqrt{3})`
`=5\sqrt{4}-4-\sqrt{6}+5-2\sqrt{2}-\sqrt{3}`
`=3\sqrt{2}+1-\sqrt{6}-sqrt{3}`
`=3\sqrt{2}-\sqrt{3}-(\sqrt{6}-1)`
`=\sqrt{3}(\sqrt{6}-1)-(\sqrt{6}-1)`
`=(\sqrt{6}-1)(\sqrt{3}-1)`
Do đó `B=(sqrt{2}+1)(5-2\sqrt{2}-\sqrt{3})(\sqrt{3}+1)(\sqrt{6}+1)`
`=(\sqrt{6}-1)(\sqrt{3}-1)(\sqrt{3}+1)(\sqrt{6}+1)`
`=(\sqrt{6}-1)(3-1)(\sqrt{6}-1)`
`=2(\sqrt{6}-1))(\sqrt{6}+1)`
`=2(6-1)`
`=10`
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