vc 

\(c,\Rightarrow-8+0,5x=1,5\\ \Rightarrow0,5x=-9,5\Rightarrow x=-19\\ d,\Rightarrow\left(-3\right)^x=\left(-3\right)^3\left(-3\right)^4=\left(-3\right)^7\\ \Rightarrow x=7\)

hỉu j?

Bài 2:

Vì a,b là nghiệm PT nên \(\left\{{}\begin{matrix}30a^2-4a=2010\\30b^2-4b=2010\end{matrix}\right.\)

\(\Rightarrow N=\dfrac{a^{2008}\left(30a^2-4a\right)+b^{2008}\left(30b^2-4b\right)}{a^{2008}+b^{2008}}\\ \Rightarrow N=\dfrac{a^{2008}\cdot2010+b^{2008}\cdot2010}{a^{2008}+b^{2008}}=2010\)

Bài 1:

Viét: \(\left\{{}\begin{matrix}x_1+x_2=a\\x_1x_2=a-1\end{matrix}\right.\)

\(M=\dfrac{2x_1^2+x_1x_2+2x_2^2}{x_1^2x_2+x_1x_2^2}=\dfrac{2\left(x_1+x_2\right)^2-3x_1x_2}{x_1x_2\left(x_1+x_2\right)}=\dfrac{2a^2-3a+3}{a^2-a}\)

Bài 5:

\(a,3A=3^2+3^3+...+3^{101}\\ \Rightarrow3A-A=3^2+3^3+...+3^{101}-3-3^2-...-3^{100}\\ \Rightarrow2A=3^{101}-3\\ \Rightarrow2A+3=3^{101}=3^{4n+1}\\ \Rightarrow4n+1=101\\ \Rightarrow n=25\)

\(b,x^2+1=6y^2+2\\ \Rightarrow x^2=6y^2+1\)

\(\Rightarrow x\) lẻ

Mà \(x^2-1=6y^2\Rightarrow\left(x-1\right)\left(x+1\right)=6y^2\)

Mà x lẻ nên \(\left(x-1\right)\left(x+1\right)⋮8\Rightarrow6y^2⋮8\Rightarrow y\in B\left(2\right)\)

Mà y nguyên tố nên \(y=2\)

\(\Rightarrow x^2-24=1\Rightarrow x^2=25\Rightarrow x=5\left(snt\right)\)

Vậy \(\left(x;y\right)=\left(5;2\right)\)

24/12/2021 nhục vc

\(a,x=3\Leftrightarrow9-12+m+1=0\Leftrightarrow m=2\\ b,\text{PT có 2 nghiệm pb }\Leftrightarrow\Delta'=4-\left(m+1\right)>0\\ \Leftrightarrow m< 3\\ \text{Viét: }\left\{{}\begin{matrix}x_1+x_2=4\\x_1x_2=m+1\end{matrix}\right.\\ \dfrac{x_1}{x_2}+\dfrac{x_2}{x_1}=1\\ \Leftrightarrow\dfrac{x_1^2+x_2^2}{x_1x_2}=1\\ \Leftrightarrow x_1^2+x_2^2-x_1x_2=0\\ \Leftrightarrow\left(x_1+x_2\right)^2-3x_1x_2=0\\ \Leftrightarrow16-3m-3=0\\ \Leftrightarrow m=\dfrac{13}{3}\left(ktm\right)\Leftrightarrow m\in\varnothing\)

Đặt \(d=ƯCLN\left(2n+3,3n+5\right)\)

\(\Rightarrow2n+3⋮d;3n+5⋮d\\ \Rightarrow2\left(3n+5\right)-3\left(2n+3\right)=1⋮d\\ \Rightarrow d=1\\ \RightarrowƯCLN\left(2n+3,3n+5\right)=1\\ \RightarrowĐpcm\)

Bán kính hồ là \(31,4:3,14:2=5\left(m\right)\)

Diện tích hồ là \(5\times5\times3,14=78,5\left(m^2\right)\)

Cạnh khu đất là \(240:4=60\left(m\right)\)

Diện tích khu đất là \(60\times60=3600\left(m^2\right)\)

Diện tích còn lại là \(3600-78,5=3521,5\left(m^2\right)\)