a) \(11x-20< 4+5x\)

\(\Leftrightarrow11x-5x< 4+20\)

\(\Leftrightarrow6x< 24\)

\(\Leftrightarrow x< 4\)

b) \(\left(x-3\right)\left(x+3\right)< \left(x+2\right)^2+3\)

\(\Leftrightarrow x^2-9< x^2+4x+4+3\)

\(\Leftrightarrow x^2-9< x^2+4x+7\)

\(\Leftrightarrow x^2-x^2-4x< 7+9\)

\(\Leftrightarrow-4x< 16\)

\(\Leftrightarrow x< -4\)

c) \(\dfrac{2x+1}{2}+3\ge\dfrac{3x-5}{3}-\dfrac{4x+1}{4}\)

\(\Leftrightarrow\dfrac{6\left(2x+1\right)}{12}+\dfrac{36}{12}\ge\dfrac{4\left(3x-5\right)}{12}-\dfrac{3\left(4x+1\right)}{12}\)

\(\Leftrightarrow12x+6+36\ge12x-20-12x-3\)

\(\Leftrightarrow12x+42\ge-23\)

\(\Leftrightarrow12x\ge-23-42\)

\(\Leftrightarrow12x\ge-65\)

\(\Leftrightarrow x\ge-\dfrac{65}{12}\)

a) \(4x^2+16x+3=0\)

\(\Delta'=84-12=72\Rightarrow\sqrt[]{\Delta'}=6\sqrt[]{2}\)

Phương trình có 2 nghiệm

\(\left[{}\begin{matrix}x=\dfrac{-8+6\sqrt[]{2}}{4}\\x=\dfrac{-8-6\sqrt[]{2}}{4}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-2\left(4-3\sqrt[]{2}\right)}{4}\\x=\dfrac{-2\left(4+3\sqrt[]{2}\right)}{4}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-\left(4-3\sqrt[]{2}\right)}{2}\\x=\dfrac{-\left(4+3\sqrt[]{2}\right)}{2}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3\sqrt[]{2}-4}{2}\\x=\dfrac{-3\sqrt[]{2}-4}{2}\end{matrix}\right.\)

b) \(7x^2+16x+2=1+3x^2\)

\(4x^2+16x+1=0\)

\(\Delta'=84-4=80\Rightarrow\sqrt[]{\Delta'}=4\sqrt[]{5}\)

Phương trình có 2 nghiệm

\(\left[{}\begin{matrix}x=\dfrac{-8+4\sqrt[]{5}}{4}\\x=\dfrac{-8-4\sqrt[]{5}}{4}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-4\left(2-\sqrt[]{5}\right)}{4}\\x=\dfrac{-4\left(2+\sqrt[]{5}\right)}{4}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\left(2-\sqrt[]{5}\right)\\x=-\left(2+\sqrt[]{5}\right)\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-2+\sqrt[]{5}\\x=-2-\sqrt[]{5}\end{matrix}\right.\)

c) \(4x^2+20x+4=0\)

\(\Leftrightarrow4\left(x^2+5x+1\right)=0\)

\(\Leftrightarrow x^2+5x+1=0\)

\(\Delta=25-4=21\Rightarrow\sqrt[]{\Delta}=\sqrt[]{21}\)

Phương trình có 2 nghiệm

\(\left[{}\begin{matrix}x=\dfrac{-5+\sqrt[]{21}}{2}\\x=\dfrac{-5-\sqrt[]{21}}{2}\end{matrix}\right.\)

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