Question

\(x^3\left(x\text{-}5\right)+3x\left(x\text{-}5\right)=0\)

Answer 1

x². x(x-5) + 3x(x-5) = 0

=> x(x-5) (x² + 3) = 0

Vì x² + 3 \(\ge\)3 => x(x+5) = 0

=> \(\left[{}\begin{matrix}x=0\\x=5\end{matrix}\right.\)

Answer 2

\(x^3\left(x-5\right)+3x\left(x-5\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left(x^3+3x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x^3+3x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x\left(x^2+3\right)=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=0\\x^2=-3\left(vô-lí\right)\end{matrix}\right.\)Vậy x=5; x=0

Answer 3

x³(x-5)+3x(x-5)=0

x².x(x-5)+3x(x-5)=0

x(x-5)(x²+3)=0

Nếu x²+3=0 thì:

x²=3\(\Rightarrow\)không tồn tại giá trị x

Nếu x(x-5)=0 thì:

\(\Leftrightarrow x=0\)

\(\Leftrightarrow x-5=0\Rightarrow x=5\)

Answer 4

x³.(x-5) + 3x( x-5)=0

x⁴-5.x³+(x²+3) = 0

x.(x-5) + (x²+3)=0

Vì x²+3 lớn hơn hoặc bằng 0 => x( x+5) =0

=>x=0 hoặc x=5

Suy ra : x=0 hoặc x=5 ( Hoàn Thành Việc Chứng Minh )

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Answer 5

x².x(x-5) + 3x(x-5) = 0

=> x(x-5)(x² + 3) = 0

=> \(\left[{}\begin{matrix}x\left(x-5\right)=0\\x^2+3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x-5=0\\x^2=-3\end{matrix}\right.\Rightarrow}\left[{}\begin{matrix}x=0\\x=5\\x\in\varnothing\end{matrix}\right.\)Vậy x = 5 hoặc x = 0