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Bài 209 : đăng tách ra cho mn cùng làm nhé
a,sửa đề : \(A=\left(3x+1\right)^2-2\left(3x+1\right)\left(3x+5\right)+\left(3x+5\right)^2\)
\(=\left(3x+1-3x-5\right)^2=\left(-4\right)^2=16\)
b, \(B=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{32}+1\right)\)
\(2B=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{32}+1\right)=\left(3^{32}-1\right)\left(3^{32}+1\right)\)
\(2B=3^{64}-1\Rightarrow B=\frac{3^{64}-1}{2}\)
c, \(C=\left(a+b-c\right)^2+\left(a-b+c\right)^2-2\left(b-c\right)^2\)
\(=2\left(a-b+c\right)^2-2\left(b-c\right)^2=2\left[\left(a-b+c\right)^2-\left(b-c\right)^2\right]\)
\(=2\left(a-b+c-b+c\right)\left(a-b+c+b-c\right)=2a\left(a-2b+2c\right)\)
a) \(\left(4x-1\right)^2-\left(x+2\right)^2=0\)
\(\Leftrightarrow\left(4x-1+x+2\right)\left(4x-1-x-2\right)=0\)
\(\Leftrightarrow\left(5x+1\right)\left(3x-3\right)=0\)
\(\Leftrightarrow3\left(5x+1\right)\left(x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}5x+1=0\\x-1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{5}\\x=1\end{cases}}\)
b) \(x^2-7x=8\Leftrightarrow x^2-7x-8=0\)
\(\Leftrightarrow x^2+x-8x-8=0\)
\(\Leftrightarrow x\left(x+1\right)-8\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-8\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+1=0\\x-8=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=8\end{cases}}\)
c) \(\left(5x-7\right)^2-25=0\Leftrightarrow\left(5x-7-5\right)\left(5x-7+5\right)=0\)
\(\Leftrightarrow\left(5x-12\right)\left(5x-2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}5x-12=0\\5x-2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{12}{5}\\x=\frac{2}{5}\end{cases}}\)
Vì EF // GH nên góc E + góc H = 1800 ( trong cùng phía )
=> góc H = 1800 - góc E = 1800 - 750 = 1050
Vì EF // GH => góc F + góc G = 1800
=> góc G = 1800 - góc F = 1800 - 1150 = 650
3x2 - 5x -2 =0
3x2 - 6x + x -2=0
3x(x - 2) + (x-2)=0
(x-2)(3x+1)=0
\(\orbr{\begin{cases}x-2=0\\3x+1=0\end{cases}}\)
\(\orbr{\begin{cases}x=2\\x=-\frac{1}{3}\end{cases}}\)
Vậy x = 2 hoặc x = -1/3
3x^2 - 5x + 2 = 0
3x^2 - 6x + x - 2 = 0
3x*(x-2) + 1*(x-2) = 0
(x-2)*(3x+1) = 0
x - 2 = 0 hoặc 3x + 1 = 0
x = 0 + 2 hoặc 3x = -1
x = 2 hoặc x = -1/3