Question

Answer 1

a)x²-6x=0

⇔x(x-6)=0

\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\x=6\end{matrix}\right.\)

b)x³-25x=0

⇔x(x²-25)=0

⇔x(x-5)(x+5)=0

\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\x=5\\x=-5\end{matrix}\right.\)

c)(2x-5)²-x(2x-5)=0

⇔ (2x-5)(x-5)=0

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{2}\\x=5\end{matrix}\right.\)

Answer 2

a) \(x^2-6x=0\Rightarrow x\left(x-6\right)=0\Rightarrow\left[{}\begin{matrix}x=0\\x-6=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=6\end{matrix}\right.\)

b) \(x^3-25x=0\Rightarrow x\left(x^2-25\right)=0\Rightarrow x\left(x-5\right)\left(x+5\right)=0\Rightarrow\left[{}\begin{matrix}x=0\\x=5\\x=-5\end{matrix}\right.\)

c) \(\left(2x-5\right)^2-x\left(2x-5\right)=0\Rightarrow\left(2x-5\right)\left(2x-5-x\right)=0\Rightarrow\left[{}\begin{matrix}2x-5=0\\x-5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=5\end{matrix}\right.\)

d)\(\left(3x-1\right)^2-\left(x+3\right)^2=0\Rightarrow\left(3x-1-x-3\right)\left(3x-1+x+3\right)=0\Rightarrow\left[{}\begin{matrix}2x-4=0\\4x+2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{1}{2}\end{matrix}\right.\)

e) \(x^2+2x-15=0\Rightarrow\left(x-3\right)\left(x+5\right)=0\Rightarrow\left[{}\begin{matrix}x-3=0\\x+5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=-5\end{matrix}\right.\)

Answer 3

d)(3x-1)²-(x+3)²=0

⇔(2x-4)(4x+2)=0

⇔4(x-2)(2x+1)=0

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

e) x²+2x-15=0

⇔ (x+5)(x-3)=0

\(\Leftrightarrow\left\{{}\begin{matrix}x=-5\\x=3\end{matrix}\right.\)

Answer 4

a: Ta có: \(x^2-6x=0\)

\(\Leftrightarrow x\left(x-6\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=6\end{matrix}\right.\)

b: Ta có: \(x^3-25x=0\)

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

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

c: Ta có: \(\left(2x-5\right)^2-x\left(2x-5\right)=0\)

\(\Leftrightarrow\left(2x-5\right)\left(x-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=5\end{matrix}\right.\)

d: Ta có: \(\left(3x-1\right)^2-\left(x+3\right)^2=0\)

\(\Leftrightarrow\left(3x-1-x-3\right)\left(3x-1+x+3\right)=0\)

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

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

e: Ta có: \(x^2+2x-15=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=3\end{matrix}\right.\)