Toán Lớp 8: a, x ²-x=0 b, 5x ²+30x=0 c, 2x ²=8x d, 9x ²-4=0 e, 16=25x ² g,3x(x+1)+(x+1)(x-3)=0 h, (x-2)(3x-5)-(x-2)(x+1)=0 Trả lời chi tiết đầy đủ

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1. Giải đáp+Lời giải và giải thích chi tiết:

   a, x ^2-x=0

   <=>x(x-1)=0

   <=>$\left[\begin{matrix} x=0\\ x-1=0\end{matrix}\right.$

   <=>$\left[\begin{matrix} x=0\\ x=1\end{matrix}\right.$

   Vậy x_1=0;x_2=1

   b, 5x ^2+30x=0

   <=>5x(x+6)=0

   <=>$\left[\begin{matrix} 5x=0\\ x+6=0\end{matrix}\right.$

   <=>$\left[\begin{matrix} x=0\\ x=-6\end{matrix}\right.$

   Vậy x_1=0;x_2=-6

   c, 2x ^2=8x

   <=>2x^2-8x=0

   <=>2x(x-4)=0

   <=>$\left[\begin{matrix} 2x=0\\ x-4=0\end{matrix}\right.$

   <=>$\left[\begin{matrix} x=0\\ x=4\end{matrix}\right.$

   Vậy x_1=0;x_2=4

   d, 9x ^2-4=0

   <=>(3x-2)(3x+2)=0

   <=>$\left[\begin{matrix} 3x-2=0\\ 3x+2=0\end{matrix}\right.$

   <=>$\left[\begin{matrix} 3x=2\\ 3x=-2\end{matrix}\right.$

   <=>$\left[\begin{matrix} x=2/3\\ x=-2/3\end{matrix}\right.$

   Vậy x_1=2/3;x_2=-2/3

   e, 16=25x^2

   <=>16-25x^2=0

   <=>(4-5x)(4+5x)=0

   <=>$\left[\begin{matrix} 4-5x=0\\4+5x=0\end{matrix}\right.$

   <=>$\left[\begin{matrix} 5x=4\\5x=-4\end{matrix}\right.$

   <=>$\left[\begin{matrix} x=4/5\\x=-4/5\end{matrix}\right.$

   Vậy x_1=4/5;x_2=-4/5

   g,3x(x+1)+(x+1)(x-3)=0

   <=>(x+2)[3x+(x-3)]=0

   <=>(x+2)[3x+x-3]=0

   <=>(x+2)(4x-3)=0

   <=>$\left[\begin{matrix} x+2=0\\4x-3=0\end{matrix}\right.$

   <=>$\left[\begin{matrix} x=-2\\4x=3\end{matrix}\right.$

   <=>$\left[\begin{matrix} x=-2\\x=3/4\end{matrix}\right.$

   h, (x-2)(3x-5)-(x-2)(x+1)=0

   <=>(x-2)[(3x-5)-(x+1)=0

   <=>(x-2)(3x-5-x-1)=0

   <=>(x-2)(2x-6)=0

   <=>2(x-2)(x-3)=0

   <=>$\left[\begin{matrix} x-2=0\\x-3=0\end{matrix}\right.$

   <=>$\left[\begin{matrix} x=2\\x=3\end{matrix}\right.$

   Vậy x_1=2;x_2=3

   Trả lời
2. $\text{a) x² – x = 0}$

   $\text{⇔ x(x – 1) = 0}$

   $\text{⇔ $\left[\begin{matrix} x = 0\\ x – 1 = 0\end{matrix}\right.$}$

   $\text{⇔ $\left[\begin{matrix} x = 0\\ x = 1\end{matrix}\right.$}$

   $\text{Vậy x ∈ {0; 1}}$

   $\text{b) 5x² + 30x = 0}$

   $\text{⇔ 5x(x + 6) = 0}$

   $\text{⇔ $\left[\begin{matrix} 5x = 0\\ x + 6 = 0\end{matrix}\right.$}$

   $\text{⇔ $\left[\begin{matrix} x = 0\\ x = -6\end{matrix}\right.$}$

   $\text{Vậy x ∈ {0; -6}}$

   $\text{c) 2x² = 8x}$

   $\text{⇔ 2x² – 8x = 0}$

   $\text{⇔ 2x(x – 4) = 0}$

   $\text{⇔ $\left[\begin{matrix} 2x = 0\\ x – 4 = 0\end{matrix}\right.$}$

   $\text{⇔ $\left[\begin{matrix} x = 0\\ x = 4\end{matrix}\right.$}$

   $\text{Vậy x ∈ {0; 4}}$

   $\text{d) 9x² – 4 = 0}$

   $\text{⇔ (3x – 2)(3x + 2) = 0}$

   $\text{⇔ $\left[\begin{matrix} 3x – 2 = 0\\3x + 2 = 0\end{matrix}\right.$}$

   $\text{⇔ $\left[\begin{matrix} x = \dfrac{2}{3}\\ x = -\dfrac{2}{3}\end{matrix}\right.$}$

   $\text{Vậy x ∈ {±$\dfrac{2}{3}$}}$

   $\text{e) 16 = 25x²}$

   $\text{⇔ 16 – 25x² = 0}$

   $\text{⇔ (4 – 5x)(4 + 5x) = 0}$

   $\text{⇔ $\left[\begin{matrix} 4 – 5x = 0\\4 + 5x = 0\end{matrix}\right.$}$

   $\text{⇔ $\left[\begin{matrix} x = \dfrac{4}{5}\\ x = -\dfrac{4}{5}\end{matrix}\right.$}$

   $\text{Vậy x ∈ {±$\dfrac{4}{5}$}}$

   $\text{g) 3x(x + 1) + (x + 1)(x – 3) = 0}$

   $\text{⇔ (x + 1)(3x + x – 3) = 0}$

   $\text{⇔ (x + 1)(4x – 3) = 0}$

   $\text{⇔ $\left[\begin{matrix} x + 1 = 0\\4x – 3 = 0\end{matrix}\right.$}$

   $\text{⇔ $\left[\begin{matrix} x = -1\\ x = \dfrac{3}{4}\end{matrix}\right.$}$

   $\text{Vậy x ∈ {-1; $\dfrac{3}{4}$}}$

   $\text{h) (x – 2)(3x – 5) – (x – 2)(x + 1) = 0}$

   $\text{⇔ (x – 2)(3x – 5 – x – 1) = 0}$

   $\text{⇔ (x – 2)(2x – 6) = 0}$

   $\text{⇔ $\left[\begin{matrix} x  – 2 = 0\\2x – 6 = 0\end{matrix}\right.$}$

   $\text{⇔ $\left[\begin{matrix} x = 2\\ x = 3\end{matrix}\right.$}$

   $\text{Vậy x ∈ {2; 3}}$

   $\textit{Ha1zzz}$

   Trả lời