a/ Xét pt :

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

\(\Delta'=\left(m-1\right)^2-\left(2m-5\right)=m^2-2m+1-2m+5=m^2-4m+6=\left(m-2\right)^2+2>0\forall m\)

\(\Leftrightarrow\) pt luôn có 2 nghiệm pb với mọi m

b/ Phương trình cớ 2 nghiệm trái dấu

\(\Leftrightarrow2m-5< 0\)

\(\Leftrightarrow m< \dfrac{5}{2}\)

c/ Theo định lí Vi - et ta có :

\(\left\{{}\begin{matrix}x_1+x_2=2\left(m-1\right)\\x_1.x_2=2m-5\end{matrix}\right.\)

\(A=x_1^2+x_2^2\)

\(=\left(x_1+x_2\right)^2-2x_1.x_2\)

\(=4\left(m-1\right)^2-2\left(2m-5\right)\)

\(=4m^2-8m+4-4m+10\)

\(=4m^2-12m+14=4\left(m^2-3m+\dfrac{9}{4}\right)+5=4\left(m-\dfrac{3}{2}\right)^2+5\ge5\)

\(A_{min}=5\Leftrightarrow m=\dfrac{3}{2}\)

\(A=444......4\) (\(2n\) chữ số 4) \(=4.1111.....111\) (\(2n\) chữ số 1) \(=4.\dfrac{10^{2n}-1}{9}\)

\(B=222.....22\) (\(n+1\) chữ số 2) \(=2.111....11\) (\(n+1\) chữ số 1) \(=2.\dfrac{10^{n+1}-1}{9}\)

\(C=888....888\) (\(n\) chữ số 8) \(=8.111....1111\) (\(n\) chữ số 1) \(=8.\dfrac{10^n-1}{9}\)

\(\Leftrightarrow A+B+C+7=\dfrac{4,10^{2n}+2.10^{n+1}+8.10^n-14}{9}\)

Xét \(\Delta AMN\) có : \(AM+AN>MN\)

Xét  \(\Delta ABC\) có : \(AB+AC>BC\)

Mà \(\left\{{}\begin{matrix}AM< AB\\AN< AC\end{matrix}\right.\) \(\Leftrightarrow AB+AC>AM+AN\)

\(\Leftrightarrow BC>MN\)

\(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt{x^2+3x+5}}{4x-1}=\lim\limits_{x\rightarrow-\infty}\dfrac{\left|x\right|\sqrt{1+\dfrac{3}{x}+\dfrac{5}{x^2}}}{x\left(4-\dfrac{1}{x}\right)}=\dfrac{-1}{4}\)

Bạn tự vẽ hình nhé ^ ^ 

a/ Ta có : \(\Delta ABC\) cân tại A \(\Leftrightarrow\widehat{B}=\widehat{C}\)

Xét \(\Delta BCN;\Delta CBM\) có :

\(\left\{{}\begin{matrix}\widehat{B}=\widehat{C}\\BCchung\\\widehat{BNC}=\widehat{BMC}=90^0\end{matrix}\right.\)

\(\Leftrightarrow\Delta BCN=\Delta CBM\left(ch-gn\right)\)

\(\Leftrightarrow BM=CN\)

b/ Xét \(\Delta ABM;\Delta ACN\) có :

\(\left\{{}\begin{matrix}\widehat{A}chung\\\widehat{BMA}=\widehat{ANC}=90^0\\BM=CN\end{matrix}\right.\)

\(\Leftrightarrow\Delta ABM=\Delta ACN\left(ch-gn\right)\)

\(\Leftrightarrow AM=AN\)

\(\Leftrightarrow\Delta AMN\) cân

Mọi người hãy vote cho mình nhaaa =)))) iu iu 

a/ Xét pt : \(\left\{{}\begin{matrix}mx-y=1\\\dfrac{x}{2}-\dfrac{y}{2}=335\end{matrix}\right.\)

 Khi \(m=2\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x-y=1\\x-y=670\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=-669\\y=-1339\end{matrix}\right.\)

b/ \(\left\{{}\begin{matrix}mx-y=1\\x-y=670\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}y=x-670\\mx-\left(x-670\right)=1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}y=x-670\\x\left(m-1\right)=-669\end{matrix}\right.\)

Để pt có nghiệm duy nhất \(\Leftrightarrow m\ne1\)

Vậy...

\(t=1h3p=3780\left(s\right)\)

\(A=P.t=3024000\left(J\right)\)

\(P_{nc}=\dfrac{A}{h}=549818,18\left(N\right)\)

\(m=\dfrac{P_n}{10}=54981,81\left(kg\right)\)