Tìm nghiệm: f(x)=3x-6 g(x)=-5x² + 30x h(x)=(x-3)(16-4x) k(x)=2x³ -32x m(x)=x²+7x-8 n(x)=5x²+9x+4

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1. $f(x)=3x-6=0$

   ⇒ $3x=6$

   ⇒ $x=2$

   $g(x)=-5x^2+30x=0$

   ⇒\(\left[ \begin{array}{l}x=0\\-5x+30=0\end{array} \right.\) $x.(-5x+30)=0$

   ⇒\(\left[ \begin{array}{l}x=0\\x=6\end{array} \right.\)

   $h(x)=(x-3)(16-4x)=0$

   ⇒\(\left[ \begin{array}{l}x-3=0\\16-3x=0\end{array} \right.\)

   ⇒\(\left[ \begin{array}{l}x=3\\x=\dfrac{16}{3}\end{array} \right.\)

   $k(x)=2x^3-32x$

   ⇒\(\left[ \begin{array}{l}x=0\\2x^2-3=0\end{array} \right.\)

   ⇒\(\left[ \begin{array}{l}x=0\\x=\dfrac{\sqrt{6}}{2}or\dfrac{-\sqrt{6}}{2}\end{array} \right.\)

   $m(x)=x^2+7x-8$

   ⇒ $x^2+8x-x-8$

   ⇒ $x(x-1)+8.(x-1)$

   ⇒ $(x-1).(x+8)=0$

   ⇒\(\left[ \begin{array}{l}x-1=0\\x+8=0\end{array} \right.\)

   ⇒\(\left[ \begin{array}{l}x=1\\x=-8\end{array} \right.\)

   $n(x)=5x^2+9x+4$

   ⇒ $(x+1).(5x+4)=0$

   ⇒\(\left[ \begin{array}{l}x+1=0\\5x+4=0\end{array} \right.\)

   ⇒\(\left[ \begin{array}{l}x=-1\\x=\dfrac{-4}{5}\end{array} \right.\)

    

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2. Đáp án:

    $a) x=2\\
   b)  {\left[\begin{aligned}x=0\\x=6\end{aligned}\right.}\\
   c) {\left[\begin{aligned}x=3\\x=4\end{aligned}\right.}\\
   d){\left[\begin{aligned}x=0\\x=4\\ x=-4\end{aligned}\right.}\\
   e)w {\left[\begin{aligned}x=8\\x=1\end{aligned}\right.}\\
   f)  {\left[\begin{aligned}x=-1\\x=\frac{-4}{5}\end{aligned}\right.}\\$

   Giải thích các bước giải:

    $a)f(x)=3x-6=0\\
   \Leftrightarrow 3(x-2)=0\Leftrightarrow x=2\\
   b) g(x)=-5x^2+30x=0\\
   \Leftrightarrow -5x(x-6)=0\\
   \Leftrightarrow {\left[\begin{aligned}x=0\\x=6\end{aligned}\right.}\\
   c)h(x)=(x-3)(16-4x)=0\\
   \Leftrightarrow {\left[\begin{aligned}x-3=0\\16-4x=0\end{aligned}\right.}\\
   \Leftrightarrow {\left[\begin{aligned}x=3\\x=4\end{aligned}\right.}\\
   d)k(x)=2x^3-32x=0\\
   \Leftrightarrow 2x(x^2-16)=0\\
   \Leftrightarrow {\left[\begin{aligned}x=0\\x^2=16\end{aligned}\right.}\\
   \Leftrightarrow {\left[\begin{aligned}x=0\\x=4\\ x=-4\end{aligned}\right.}\\
   e)m(x)=x^2+7x-8=0\\
   \Leftrightarrow x^2+8x-x-8=0\\
   \Leftrightarrow x(x+8)-(x-8)=0\\
   \Leftrightarrow (x-8)(x-1)=0\\
   \Leftrightarrow {\left[\begin{aligned}x=8\\x=1\end{aligned}\right.}\\
   f) n(x)=5x^2+9x+4=0\\
   \Leftrightarrow 5x^2+5x+4x+4=0\\
   \Leftrightarrow 5x(x+1)+4(x+1)=0\\
   \Leftrightarrow (x+1)(5x+4)=0\\
   \Leftrightarrow {\left[\begin{aligned}x+1=0\\5x+4=0\end{aligned}\right.}\\
   \Leftrightarrow {\left[\begin{aligned}x=-1\\x=\frac{-4}{5}\end{aligned}\right.}$

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