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a) x(x-1) = 0
\(\Rightarrow\orbr{\begin{cases}x=0\\x-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=-1\end{cases}}}\)
b) tương tự
\(x^3+9x^2+27x+26=0\)
\(\Leftrightarrow\left(x+2\right)\left(x^2+7x+13\right)=0\Rightarrow x=-2\)
\(x^3+9x^2+27x+26=0\)
\(\Leftrightarrow x^3+9x^2+27x+27=1\)
\(\Leftrightarrow\left(x+3\right)^3=1^3\)
\(\Leftrightarrow x+3=1\Leftrightarrow x=-2\)
\(=\frac{3x^2+9x-3}{x^2+x-2}-\frac{x+1}{x+2}-\frac{x-2}{x-1}\)
\(=\frac{3x^2+9x-3}{\left(x+2\right)\left(x-1\right)}-\frac{\left(x+1\right)\left(x-1\right)}{\left(x+2\right)\left(x-1\right)}-\frac{\left(x-2\right)\left(x+2\right)}{\left(x-1\right)\left(x+2\right)}\)
\(=\frac{3x^2+9x-3-\left(x^2-1\right)-\left(x^2-4\right)}{\left(x-1\right)\left(x+2\right)}\)
\(=\frac{3x^2+9x-3-x^2+1-x^2+4}{\left(x-1\right)\left(x+2\right)}\)
\(=\frac{x^2+9x+2}{\left(x-1\right)\left(x+2\right)}\)
\(\left(x-3\right)^{^2}-4=0\)
\(\left(x-3\right)^2=4\)
\(\Rightarrow\hept{\begin{cases}x-3=2\\x-3=-2\end{cases}\Rightarrow\hept{\begin{cases}x=5\\x=1\end{cases}}}\)
=> (x-3)^2 = 0 + 4 = 4
=> (x-3)^2= 2^2
=> x-3= 2 hoặc -2
Nếu x-3=2 thì x= 2+3=5
Nếu x-3=-2 thì x=-2-3= -5
\(5x.\left(3x-2\right)=4-9x^2\)
\(\Rightarrow5x.\left(3x-2\right)-\left(4-9x^2\right)=0\)
\(\Rightarrow5x.\left(3x-2\right)+\left(9x^2-4\right)=0\)
\(\Rightarrow5x.\left(3x-2\right)+\left(3x-2\right).\left(3x+2\right)=0\)
\(\Rightarrow\left(3x-2\right).\left(5x+3x+2\right)=0\)
\(\Rightarrow\left(3x-2\right).\left(8x+2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}3x-2=0\\8x+2=0\end{cases}}\Rightarrow\orbr{\begin{cases}3x=2\\8x=-2\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{2}{3}\\x=\frac{-1}{4}\end{cases}}\)
Bài 1 :
a) Ta có : x2 - 9x + 8 = x2 - x - 8x + 8 = x(x - 1) - 8(x - 1) = (x - 8)(x - 1)
b) Ta có : x2 + 6x + 8 = x2 + 6x + 9 - 1 = (x + 3)2 - 1 = (x + 3 - 1)(x + 3 + 1) = (x + 2)(x + 4)
Bài 2 :
b) 4x2 - 25 = 0
=> 4x2 = 25
=> (2x)2 = 52
=> 2x = -5;5
=> x = -5/2 ; 5/2
b) = x^2 + 2.x.3 + 3^2 - 1
=(x + 3)^2 - 1
=(x + 3 + 1)(x + 3 - 1)
=(x + 4)(x + 2)
Phần a mk nghĩ bn nên tự lm.
x2+6x-7x-42=0
x(x+6)-7(x+6)=0
(x+6)(x-7)=0
x=-6 hoac x=7
( nho l ike nha)
\(9x^4-x^2=0\)
\(\Leftrightarrow x^2\left(9x^2-1\right)=0\)
\(\Leftrightarrow x^2\left(3x-1\right)\left(3x+1\right)=0\)
TH1: \(x^2=0\Rightarrow x=0\)
TH2: \(3x-1=0\Rightarrow x=\frac{1}{3}\)
TH3: \(3x+1=0\Rightarrow x=-\frac{1}{3}\)
Vậy: ....