Question

[Cao Thu Anh]

Bài 1:Cho x\(\ge0\).Tìm giá trị nhỏ nhất hoặc giá trị lớn nhất của các biểu thức sau:

1)A=3x+2\(\sqrt{x}\)+1min

2)A=x+3\(\sqrt{x}\)-3min

3)A=-2x-3\(\sqrt{x}\)+2max

4)A=-4x-5\(\sqrt{x}\)-3max

5)A=x-2\(\sqrt{x}\)+2min

6)A=x-4\(\sqrt{x}\)-5min

7)A=-x+6\(\sqrt{x}\)+5max

8)A=-x+8\(\sqrt{x}\)-10max

9)A=\(\dfrac{2}{\sqrt{x}+1}\)max

10)A=\(\dfrac{4}{\sqrt{x}+2}\)max

11)A=\(\dfrac{-3}{\sqrt{x}+3}\)min

12)A=\(\dfrac{-5}{\sqrt{x}+4}\)min

13)A=\(\dfrac{\sqrt{x}+2}{\sqrt{x}+1}\)max

14)A=\(\dfrac{\sqrt{x}+4}{\sqrt{x}+2}\)max

15)A=\(\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\)min

16)A=\(\dfrac{\sqrt{x}+2}{\sqrt{x}+4}\)min

17)A=\(\dfrac{x+3}{\sqrt{x}+1}\)min

18)A=\(\dfrac{x+5}{\sqrt{x}+2}\)min

19)A=\(\dfrac{x+12}{\sqrt{x}+2}\)min

20)A=\(\dfrac{x+7}{\sqrt{x}+3}\)min

21)A=\(\dfrac{x+9}{\sqrt{x}+4}\)min

22)A=\(\dfrac{x+24}{\sqrt{x}+5}\)min

Answer 1

[Nguyễn Lê Phước Thịnh]

1: \(=3\left(x+\dfrac{2}{3}\sqrt{x}+\dfrac{1}{3}\right)\)

\(=3\left(x+2\cdot\sqrt{x}\cdot\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{2}{9}\right)\)

\(=3\left(\sqrt{x}+\dfrac{1}{3}\right)^2+\dfrac{2}{3}>=3\cdot\dfrac{1}{9}+\dfrac{2}{3}=1\)

Dấu '=' xảy ra khi x=0

2: \(=x+3\sqrt{x}+\dfrac{9}{4}-\dfrac{21}{4}=\left(\sqrt{x}+\dfrac{3}{2}\right)^2-\dfrac{21}{4}>=-3\)

Dấu '=' xảy ra khi x=0

3: \(A=-2x-3\sqrt{x}+2< =2\)

Dấu '=' xảy ra khi x=0

5: \(=x-2\sqrt{x}+1+1=\left(\sqrt{x}-1\right)^2+1>=1\)

Dấu '=' xảy ra khi x=1