Thanks trc ạ !!! ^_^
K
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H
1 tháng 8 2021
I.
1. Are sent
2. Are given
3. Are collected
4. Aren't did
5. Are sold
6. Are taught
7. Is ask
8. Are told
9. Aren't kept
10. Are caught
Chúc bạn học tốt!! ^^
DT
Đỗ Thanh Hải
CTVVIP
5 tháng 8 2021
1 D
2 C
3 C
4 A
5 B
6 D
7 B
8 C
9 C
10 B
11 D
12 D
13 A
14 A
15 C
16 A
17 C
18 B
19 D
20 A
AT
15 tháng 7 2021
a) \(P=\dfrac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\dfrac{2x+\sqrt{x}}{\sqrt{x}}+\dfrac{2\left(x-1\right)}{\sqrt{x}-1}\left(x>0,x\ne1\right)\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{x+\sqrt{x}+1}-\dfrac{\sqrt{x}\left(2\sqrt{x}+1\right)}{\sqrt{x}}+\dfrac{2\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}-1}\)
\(=\sqrt{x}\left(\sqrt{x}-1\right)-\left(2\sqrt{x}+1\right)+2\left(\sqrt{x}+1\right)=x-\sqrt{x}+1\)
b) \(P=x-\sqrt{x}+1=\left(\sqrt{x}\right)^2-2.\sqrt{x}.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+\dfrac{3}{4}\)
\(=\left(\sqrt{x}-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\)
\(\Rightarrow P_{min}=\dfrac{3}{4}\) khi \(x=\dfrac{1}{4}\)
c) \(Q=\dfrac{2\sqrt{x}}{P}=\dfrac{2\sqrt{x}}{x-\sqrt{x}+1}\)
Ta có: \(\left\{{}\begin{matrix}2\sqrt{x}>0\left(x>0\right)\\x+\sqrt{x}+1>0\end{matrix}\right.\Rightarrow Q>0\)
Lại có: \(3x-5\sqrt{x}+3=3\left(\left(\sqrt{x}\right)^2-2.\sqrt{x}.\dfrac{5}{6}+\left(\dfrac{5}{6}\right)^2\right)+\dfrac{11}{12}\)
\(=3\left(\sqrt{x}-\dfrac{5}{6}\right)^2+\dfrac{11}{12}>0\)
\(\Rightarrow3x-5\sqrt{x}+3>0\Rightarrow3x-3\sqrt{x}+3>2\sqrt{x}\Rightarrow3\left(x-\sqrt{x}+1\right)>2\sqrt{x}\)
\(\Rightarrow3>\dfrac{2\sqrt{x}}{x-\sqrt{x}+1}\Rightarrow Q< 3\Rightarrow0< Q< 3\)
mà \(Q\in Z\Rightarrow Q\in\left\{1;2\right\}\)
Từ\(Q\) tính ta x thôi
15 tháng 7 2021
a, \(P=\dfrac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\dfrac{2x+\sqrt{x}}{\sqrt{x}}+\dfrac{2\left(x-1\right)}{\sqrt{x}-1}\)ĐK : \(x>0;x\ne1\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{x+\sqrt{x}+1}-\dfrac{2\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}}+\dfrac{2\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}-1}\)
\(=x-\sqrt{x}-2\left(\sqrt{x}+1\right)+2\left(\sqrt{x}+1\right)=x-\sqrt{x}-2\sqrt{x}-2+2\sqrt{x}+2\)
\(=x-\sqrt{x}\)
b, Ta có : \(x-\sqrt{x}+\dfrac{1}{4}-\dfrac{1}{4}=\left(\sqrt{x}-\dfrac{1}{2}\right)^2-\dfrac{1}{4}\ge-\dfrac{1}{4}\)
Dấu ''='' xảy ra khi \(x=\dfrac{1}{4}\)
Vậy GTNN P là -1/4 khi x = 1/4
c, Ta có : \(G=\dfrac{2\sqrt{x}}{P}\Rightarrow G=\dfrac{2\sqrt{x}}{x-\sqrt{x}}=\dfrac{2}{\sqrt{x}-1}\)
\(\Rightarrow\sqrt{x}-1\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)
| \(\sqrt{x}-1\) | 1 | -1 | 2 | -2 |
| \(\sqrt{x}\) | 2 | 0 | 3 | -1 |
| x | 4 | 0 ( loại ) | 9 | loại |
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