\(7x^5+\sqrt[3]{x^3+x^2+14x-13}=227\)
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)2+3(x+1)2{7x2−22x+28=(2x−1)2+3(x−3)27x2+8x+13=(2x−1)2+3(x+2)231x2+14x+4=7(2x−1)2+3(x+1)2
Do đó:
VT≥3–√|3−x|+3–√|x+2|+3–√|x+1|≥3–√(3−x)+3–√(x+2)+3–√(x+1)=33–√(x+2)VT≥3|3−x|+3|x+2|+3|x+1|≥3(3−x)+3(x+2)+3(x+1)=33(x+2)
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AHIHI
a) \(\left(x-4\right)\left(x-5\right)\left(x-6\right)\left(x-7\right)=1680\\ \Leftrightarrow\left(x-4\right)\left(x-7\right)\left(x-5\right)\left(x-6\right)=1680\\ \Leftrightarrow\left(x^2-11x+28\right)\left(x^2-11x+30\right)=1680\\ \Leftrightarrow\left(x^2-11x+29-1\right)\left(x^2-11x+29+1\right)=1680\\ \)
Đặt \(x^2-11x+29=t\), ta đc \(\left(t-1\right)\left(t+1\right)=1680\\ \Leftrightarrow t^2-1=1680\Leftrightarrow t^2=1681\Leftrightarrow t=\pm41\)
Với \(t=41\Leftrightarrow x^2-11x+28=40\Leftrightarrow\left[{}\begin{matrix}x=12\\x=-1\end{matrix}\right.\)
Với \(t=-41\Leftrightarrow x^2-11x+30=-40\)(vô no)
Vậy.....
c) \(x^4-7x^3+14x^2-7x+1=0\\ \Leftrightarrow x^2-7x+14-\frac{7}{x}+\frac{1}{x^2}=0\)
\(\Leftrightarrow\left(x^2+\frac{1}{x^2}\right)-7\left(x+\frac{1}{x}\right)+14=0\)
Đặt \(x+\frac{1}{x}=t\Rightarrow x^2+\frac{1}{x^2}=t^2-2\)
Ta đc \(t^2-2-7t+14=0\Leftrightarrow t^2-7t+12=0\)
\(\Rightarrow\left[{}\begin{matrix}t=4\\t=3\end{matrix}\right.\)
B tự giải tiếp nha
Ta có pt \(4x^2-14x-2=3\left(\sqrt{2x^2-7x+3}-2\right)\Leftrightarrow2\left(2x^2-7x-1\right)=3.\dfrac{2x^2-7x+3-4}{\sqrt{2x^2-7x+3}+2}\Leftrightarrow2\left(2x^2-7x-1\right)=3.\dfrac{2x^2-7x-1}{\sqrt{2x^2-7x+3}+2}\)
\(\Leftrightarrow\left(2x^2-7x-1\right)\left(2-\dfrac{3}{\sqrt{2x^2-7x+3}+2}\right)=0\)
Mà \(\sqrt{2x^2-7x+3}+2\ge2\Rightarrow\dfrac{3}{\sqrt{2x^2-7x+3}+2}\le\dfrac{3}{2}\Rightarrow2-\dfrac{3}{\sqrt{2x^2-7x+3}+2}>0\)
=> pt <=> \(2x^2-7x-1=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7-\sqrt{57}}{4}\\x=\dfrac{7+\sqrt{57}}{4}\end{matrix}\right.\)
\(14x\left(x+3\right)-7x^2\left(3+x\right)=\left(x+3\right)\left(14x-7x^2\right)=7x\left(2-x\right)\left(x+3\right)\\ \left(2x-5\right)\left(3+4x\right)-4x+10=\left(2x-5\right)\left(3+4x-2\right)=\left(2x-5\right)\left(4x+1\right)\)