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`

Câu hỏi trong lớp Xem thêm