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Vì 1-x-2x^2>=0>>>2x^2-x-1<=0>>>-1<=x<=1/2
F(x)=1/2(x+2√(1-2x)(x+1)<=1/2(x+1-2x+x+1)(BĐT Cô-si)
<=1/2.2=1.
Dấu= xảy ra khi 1-2x=x+1 khi x=0(TM)
Với \(x\ge-\frac{1}{2}\)
2f(x) = \(2\sqrt{\left(2x+1\right)\left(x+2\right)}+4\sqrt{x+3}-4x\)
\(=-\left(2x+1\right)+2\sqrt{\left(2x+1\right)\left(x+2\right)}-\left(x+2\right)-\left(x+3\right)+4\sqrt{x+3}-4+10\)
\(=-\left(\sqrt{2x+1}-\sqrt{x+2}\right)^2-\left(\sqrt{x+3}-2\right)^2+10\le10\)
Dấu "=" xảy ra <=> \(\hept{\begin{cases}2x+1=x+2\\x+3=4\end{cases}}\Leftrightarrow x=1\)
=> min 2f(x) = 10 tại x = 1
=> min f(x) = 5 tại x = 1
Khi \(x=1,44\): \(A=\frac{1,44+7}{\sqrt{1,44}}=\frac{8,44}{1,2}=\frac{211}{30}\)
\(B=\frac{\sqrt{x}}{\sqrt{x}+3}+\frac{2\sqrt{x}-1}{\sqrt{x}-3}-\frac{2x-\sqrt{x}-3}{x-9}\)(ĐK: \(x\ge0,x\ne9\))
\(=\frac{\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}+\frac{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}-\frac{2x-\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\frac{x-3\sqrt{x}+2x+5\sqrt{x}-3-2x+\sqrt{x}+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\frac{x+3\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\frac{\sqrt{x}}{\sqrt{x}-3}\)
\(S=\frac{1}{B}+A=\frac{\sqrt{x}-3}{\sqrt{x}}+\frac{x+7}{\sqrt{x}}=\frac{x+\sqrt{x}+4}{\sqrt{x}}=\sqrt{x}+\frac{4}{\sqrt{x}}+1\)
\(\ge2\sqrt{\sqrt{x}.\frac{4}{\sqrt{x}}}+1=5\)
Dấu \(=\)khi \(\sqrt{x}=\frac{4}{\sqrt{x}}\Leftrightarrow x=4\)(thỏa mãn)
\(A=\frac{2a-3\sqrt{a}-2}{\sqrt{a}-2}\\ =\frac{2a-4\sqrt{a}+\sqrt{a}-2}{\sqrt{a}-2}\\ =\frac{\left(2\sqrt{a}+1\right)\left(\sqrt{a}-2\right)}{\sqrt{a}-2}\\ =2\sqrt{a}+1\)
I don't now
mik ko biết
sorry
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