anh chị giải hộ em bài Toán
29+1
kb với em
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\(\dfrac{x}{a}=\dfrac{m-\dfrac{x}{2}}{m}\)
\(\Rightarrow xm=a\left(m-\dfrac{x}{2}\right)\)
\(\Rightarrow xm=am-\dfrac{ax}{2}\)
\(\Rightarrow2xm=2am-ax\)
\(\Rightarrow2xm+ax=2am\)
\(\Rightarrow x\left(2m+a\right)=2am\)
\(\Rightarrow x=\dfrac{2am}{a+2m}\)
a) 40 và 60
Ta có Ư(40)\(\in\){1;2;4;5;6;8;10;16;20}
Ư(60)\(\in\){1;2;3;4;5;6;10;12;15;20;30)
ƯC(40;60)\(\in\){1;2;3;4;5;6;10;20}
Trong đó,20 là ƯCLN.Vậy ƯCLN(40;60)\(\in\){20}
b)
\(1,\\ a,x^4-8x^2-9=0\\ \Leftrightarrow x^4+x^2-9x^2-9=0\\ \Leftrightarrow\left(x^2+1\right)\left(x^2-9\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2+1=0\\x-3=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\in\varnothing\left(x^2+1\ge1>0\right)\\x=3\\x=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\\ b,\left\{{}\begin{matrix}2\left(x-1\right)-3\left(x-3y\right)=5\\3\left(x-1\right)+5\left(x-3y\right)=-2\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}6\left(x-1\right)-9\left(x-3y\right)=15\\6\left(x-1\right)+10\left(x-3y\right)=-4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}19\left(x-3y\right)=-19\\3\left(x-1\right)+5\left(x-3y\right)=-2\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x-3y=-1\\3\left(x-1\right)-5=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-3y=-1\\x-1=-\dfrac{7}{3}\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{4}{3}\\-\dfrac{4}{3}-3y=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{4}{3}\\y=-\dfrac{1}{9}\end{matrix}\right.\)
5b.
Theo Bunhiacopxki:
\(\left(\sqrt{x\left(2x+y\right)}+\sqrt{y\left(2y+x\right)}\right)^2\le\left(x+y\right)\left(\left(2x+y\right)+\left(2y+x\right)\right)=3\left(x+y\right)^2\)
\(\Rightarrow\sqrt{x\left(2x+y\right)}+\sqrt{y\left(2y+x\right)}\le\sqrt{3}\left(x+y\right)\)
\(\Rightarrow\dfrac{x+y}{\sqrt{x\left(2x+y\right)}+\sqrt{y\left(2y+x\right)}}\ge\dfrac{x+y}{\sqrt{3}\left(x+y\right)}=\dfrac{1}{\sqrt{3}}\)
Dấu "=" xảy ra khi x=y
ukm kb đi em
Đáp án:
29+1=30