a) `7\sqrt{5}-2\sqrt{45}+3/4\sqrt{80}-\sqrt{20}`
`=7\sqrt{5}-6\sqrt{5}+3\sqrt{5}-2\sqrt{5}`
`=2\sqrt{5}`
b) `(4)/(\sqrt{11}+3)+(25)/(6-\sqrt{11})`
`=(4(\sqrt{11}-3))/((\sqrt{11}+3)(\sqrt{11}-3))+(25(6+\sqrt{11}))/((6-\sqrt{11})(6+\sqrt{11}))`
`=(4(\sqrt{11}-3))/(2)+(25(6+\sqrt{11}))/(25)`
`=2(\sqrt{11}-3)+6+\sqrt{11}`
`=2\sqrt{11}-6+6+\sqrt{11}`
`=3\sqrt{11}`
c) `\sqrt{8x+4}+\sqrt{18x+9}-\sqrt{32x+16}=2` `(x>=-1/2)`
⇔`\sqrt{4(2x+1)}+\sqrt{9(2x+1)}-\sqrt{16(2x+1)}=2`
⇔`2\sqrt{2x+1}+3\sqrt{2x+1}-4\sqrt{2x+1}=2`
⇔`\sqrt{2x+1}=2`
⇔`2x+1=4`
⇔`2x=3`
⇔`x=3/2` `(tm)`
Vậy `S={3/2}`
d) `\sqrt{25x^2-10x+1}=2` `(x∈R)`
⇔`\sqrt{(5x-1)^2}=2`
⇔`|5x-1|=2`
⇔\(\left[ \begin{array}{l}5x-1=2\\5x-1=-2\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=\dfrac{3}{5}(tm)\\x=-\dfrac{1}{5}(tm)\end{array} \right.\)
Vậy `S={3/5,-1/5}`
