\(x+\frac{2\sqrt{2}+x}{\sqrt{x^2+1}}=1\)
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a) \(A=\left(x-\frac{1}{2}\right)^2+\frac{2}{3}\)
Ta có: \(\left(x-\frac{1}{2}\right)^2\ge0\forall x\)
\(\Rightarrow\left(x-\frac{1}{2}\right)^2+\frac{2}{3}\ge0+\frac{2}{3}\forall x\)
Hay \(A\ge\frac{2}{3}\)
Dấu "=" xảy ra \(\Leftrightarrow x-\frac{1}{2}=0\)
\(\Leftrightarrow x=\frac{1}{2}\)
Vậy Min A= \(\frac{2}{3}\)\(\Leftrightarrow x=\frac{1}{2}\)
b) Ta có: \(\left(x+\frac{1}{2}\right)^2\ge0\forall x\)
\(\Rightarrow\left(x+\frac{1}{2}\right)^2+2\ge0+2\forall x\)
\(\Rightarrow\frac{4}{\left(x+\frac{1}{2}\right)^2+2}\le\frac{4}{2}=2\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x+\frac{1}{2}=0\)
\(\Leftrightarrow x=\frac{-1}{2}\)
Vậy Max B =2 \(\Leftrightarrow x=\frac{-1}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,\sqrt{\frac{5.\left(38^2-17^2\right)}{8.\left(47^2-19^2\right)}}\)
\(=\sqrt{\frac{5.\left(38-17\right)\left(38+17\right)}{8.\left(47-19\right)\left(47+19\right)}}\)
\(=\sqrt{\frac{5.21.55}{8.28.66}}\)
\(=\sqrt{\frac{5775}{14784}}=\frac{5\sqrt{231}}{2\sqrt{4370}}\)
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#)Thắc mắc :
Ở ý a) có số tự nhiên lớn hơn và nhỏ hơn 8 hả ??? đề logic :v
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\(b,x^3+6x^2+11x+6=0\)
\(\Rightarrow x^3+3x^2+3x^2+9x+2x+6=0\)
\(\Rightarrow x^2\left(x+3\right)+3x\left(x+3\right)+2\left(x+3\right)=0\)
\(\Rightarrow\left(x+3\right)\left(x^2+3x+2\right)=0\)
\(\Rightarrow\left(x+3\right)\left(x^2+2x+x+2\right)=0\)
\(\Rightarrow\left(x+3\right)\left[x\left(x+2\right)+\left(x+2\right)\right]=0\)
\(\Rightarrow\left(x+1\right)\left(x+2\right)\left(x+3\right)=0\)
\(\Rightarrow x\in\left\{-1;-2;-3\right\}\)
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