Đáp án+Giải thích các bước giải:
`1.`
`\sqrt{5}-\sqrt{48}+5\sqrt{27}-\sqrt{45}`
`=\sqrt{5}-4\sqrt{3}+15\sqrt{3}-3\sqrt{5}`
`=(15\sqrt{3}-4\sqrt{3}+(\sqrt{5}-3\sqrt{5})`
`=11\sqrt{3}-2\sqrt{5}`
`2.`
`a)`
`A=((1)/(a-\sqrt{a})+(1)/(\sqrt{a}-1)):(\sqrt{a}+1)/(a-2\sqrt{a}+1)``(đk:a>0;a\ne1)`
`=((1)/(\sqrt{a}.(\sqrt{a}-1))+(1)/(\sqrt{a}-1)):(\sqrt{a}+1)/(a-2\sqrt{a}+1)`
`=((1)/(\sqrt{a}.(\sqrt{a}-1))+(\sqrt{a})/(\sqrt{a}(\sqrt{a}-1))):(\sqrt{a}+1)/(a-2\sqrt{a}+1)`
`=(1+\sqrt{a})/(\sqrt{a}.(\sqrt{a}-1)).(a-2\sqrt{a}+1)/(\sqrt{a}+1)`
`=(1+\sqrt{a})/(\sqrt{a}.(\sqrt{a}-1)).((\sqrt{a}-1)^2)/(\sqrt{a}+1)`
`=(\sqrt{a}-1)/(\sqrt{a})`
Vậy `A=(\sqrt{a}-1)/(\sqrt{a})`
`b)`
`A≤(1)/(2)` `(a>0;a\ne1)`
`⇔(\sqrt{a}-1)/(\sqrt{a})≤(1)/(2)`
`⇔(\sqrt{a}-1)/(\sqrt{a})-(1)/(2)≤0`
`⇔(2\sqrt{a}-2-\sqrt{a})/(2\sqrt{a})≤0`
`⇔\sqrt{a}-2≤0`
`⇔\sqrt{a}≤2`
`⇔a≤4`
KH điều kiện `a>1`
`⇔1<a≤4`
Vậy `A≤(1)/(2)` khi `1<a≤4`
