Đáp án + Giải thích các bước giải:
`1. sqrt{7+4sqrt3} - sqrt{(5-sqrt3)^2} + \root[3]{-8}`
`= sqrt{(sqrt3)^2+4sqrt3+(sqrt4)^2} - (5-sqrt3) + (-2)`
`= sqrt{(sqrt3+2)^2} - (5-sqrt3) - 2`
`= sqrt3 + 2 - (5-sqrt3) - 2`
`= sqrt3 - 5 + sqrt3`
`= 2sqrt3 - 5`
`2. sqrt{4(x^2-2x+1)} = 6`
`⇔ sqrt{4(x^2-2x*1+1^2)} = 6`
`⇔ sqrt{4(x-1)^2} = 6`
`⇔ sqrt{2^2}sqrt{(x-1)^2} = 6`
`⇔ 2|x-1|=6`
`⇔ |x-1| = 3`
`⇔`\(\left[ \begin{array}{l}x-1=3\\x-1=-3\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=4\\x=-2\end{array} \right.\)
Vậy `S = {-2,4}`
