Đáp án:
a) `A=sqrt(3+sqrt(5+2sqrt(3))) . sqrt(3-sqrt(5+2sqrt(3)))=sqrt(3)-1`
b) `B=sqrt(4+sqrt(8)).sqrt(2+sqrt(2+sqrt(2))).sqrt(2-sqrt(2+sqrt(2)))=2`
Giải thích các bước giải:
a) `A=sqrt(3+sqrt(5+2sqrt(3))) . sqrt(3-sqrt(5+2sqrt(3)))`
`=sqrt((3+sqrt(5+2sqrt(3))).(3-sqrt(5+2sqrt(3))))`
`=sqrt(3^2-(sqrt(5+2sqrt(3)))^2)`
`=sqrt(9-5-2sqrt(3))`
`=sqrt(4-2sqrt(3))`
`=sqrt(3-2sqrt(3)+1)`
`=sqrt((sqrt(3)-1)^2)`
`=|sqrt(3)-1|`
`=sqrt(3)-1` (Vì `sqrt(3)>1` nên bt luôn dương)
b) `B=sqrt(4+sqrt(8)).sqrt(2+sqrt(2+sqrt(2))).sqrt(2-sqrt(2+sqrt(2)))`
`=sqrt(4+sqrt(8)).sqrt((2+sqrt(2+sqrt(2))).(2-sqrt(2+sqrt(2))))`
`=sqrt(4+sqrt(8)).sqrt(2^2-(sqrt(2+sqrt(2)))^2`
`=sqrt(4+sqrt(8)).sqrt(4-2-sqrt(2)`
`=sqrt((4+sqrt(8)).(2-sqrt(2))`
`=sqrt(8-4sqrt(2)+2.2sqrt(2)-sqrt(16))`
`=sqrt(8-4)`
`=sqrt(4)`
`=2`
cho mk câu trả lời hay nhất với ạ
mk xin bn đó
