5x+:hết cho x+2
tìm x ☺
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\(P\left(\dfrac{1}{2}\right)+Q\left(\dfrac{1}{2}\right)=-5.\left(\dfrac{1}{2}\right)^3+3\left(\dfrac{1}{2}\right)^2+\dfrac{2}{2}+5-5\left(\dfrac{1}{2}\right)^3+6\left(\dfrac{1}{2}\right)^2+\dfrac{2}{2}+5\)
\(P\left(\dfrac{1}{2}\right)+Q\left(\dfrac{1}{2}\right)=-\dfrac{5.1}{8}+\dfrac{3.1}{4}+6-\dfrac{5.1}{8}+\dfrac{6.1}{4}+6\)
\(P\left(\dfrac{1}{2}\right)+Q\left(\dfrac{1}{2}\right)=-\dfrac{5}{8}+\dfrac{3}{4}+6-\dfrac{5}{8}+\dfrac{3}{2}+6\)
\(P\left(\dfrac{1}{2}\right)+Q\left(\dfrac{1}{2}\right)=13\)
\(x^3+3x^2+x+a=x^2\left(x-2\right)+5x\left(x-2\right)+11\left(x-2\right)+22+a=\left(x-2\right)\left(x^2+5x+11\right)+22+a⋮\left(x-2\right)\)
\(\Rightarrow22+a=0\Rightarrow a=-22\)
a, \(Chof\left(x\right)=0\Rightarrow\left[{}\begin{matrix}x=3\\x=4\end{matrix}\right.\)
- Lập bảng xét dấu :
Vậy \(\left\{{}\begin{matrix}f\left(x\right)>0\Leftrightarrow x\in\left(3;4\right)\\f\left(x\right)< 0\Leftrightarrow x\in\left(-\infty;3\right)\cup\left(4;+\infty\right)\\f\left(x\right)=0\Leftrightarrow x\in\left\{3;4\right\}\end{matrix}\right.\)
b, \(f\left(x\right)=\left(x-1\right)\left(x+6\right)\)
( Làm tương tự câu a )
\(3x^2-6x-5x+5x^2-8x^2+24\)
\(=\left(3x^2+5x^2-8x^2\right)-\left(6x+5x\right)+24\)
\(=-11x+24\)
\(f\left(x\right)=3\Leftrightarrow\left|x-1\right|+2=3\Leftrightarrow\left|x-1\right|=1\\ \Leftrightarrow\left[{}\begin{matrix}x-1=1\\1-x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\)
\(\)áp dụng BĐT AM-GM(BÀi này ko có Max chỉ có Min)
\(=>\dfrac{1}{x}+\dfrac{1}{y}\ge2\sqrt{\dfrac{1}{xy}}=\dfrac{2}{\sqrt{xy}}\)
\(=>\dfrac{1}{2}\ge\dfrac{2}{\sqrt{xy}}=>\sqrt{xy}\ge4\)
\(=>S=\sqrt{x}+\sqrt{y}\ge2\sqrt{4}=4\)
dấu"=" xảy ra<=>x=y=4
3
giải chi tiết ra bn-_-