Question

tìm x , biết :

a, ( x mũ 3 - 4 x mũ 2 ) - ( x -4 ) = 0

b, x mũ 5 - 9x = 0

c, ( x mxu 3 - x mũ 2 ) mũ 2 - 4 x mũ 2 + 8x - 4 = 0

 

Answer 1

a/

\(x^3-4x^2-\left(x-4\right)=0\)

\(\Leftrightarrow x^2\left(x-4\right)-\left(x-4\right)=0\)

\(\Leftrightarrow\left(x-4\right)\left(x^2-1\right)=0\)

\(\Leftrightarrow\left(x-4\right)\left(x-1\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x-1=0\\x+1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=1\\x=-1\end{matrix}\right.\)

b/

\(x^5-9x=0\)

\(\Leftrightarrow x\left(x^4-9\right)=x\left(x^2-3\right)\left(x^2+3\right)=0\)

\(\Leftrightarrow x\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\sqrt{3}\\x=-\sqrt{3}\end{matrix}\right.\)

c/

\(\left(x^3-x^2\right)^2-4x^2+8x-4=0\)

\(\Leftrightarrow x^4\left(x-1\right)^2-4\left(x-1\right)^2=0\)

\(\Leftrightarrow\left(x-1\right)^2\left(x^4-4\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x^2-2=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\pm\sqrt{2}\end{matrix}\right.\)

Answer 2

Sos

 

Answer 3

giúp với mn

 

Answer 4

Cảm ơn bạn 

 

Answer 5

a) \(\left(x^3-4x^2\right)-\left(x-4\right)=0\)

\(\Rightarrow x^2\left(x-4\right)-\left(x-4\right)=0\)

\(\Rightarrow\left(x-4\right)\left(x^2-1\right)=0\)

\(\Rightarrow\left(x-4\right)\left(x-1\right)\left(x+1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-4=0\\x+1=0\\x-1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=4\\x=-1\\x=1\end{matrix}\right.\)

b) \(x^5-9x=0\)

\(\Rightarrow x\left(x^4-9\right)=0\)

\(\Rightarrow x\left(x^2-3\right)\left(x^2+3\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x^2-3=0\\x^2+3=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x^2=3\\x^2=-3\left(loại\right)\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x=\pm\sqrt[]{3}\end{matrix}\right.\)