0
0
Hãy luôn nhớ cảm ơn và vote 5*
nếu câu trả lời hữu ích nhé!
1693
1680
#andy
\[\begin{array}{l}
a)7x\left( {x - 4} \right) - x + 4 = 0\\
\Leftrightarrow 7x\left( {x - 4} \right) - \left( {x - 4} \right) = 0\\
\Leftrightarrow \left( {7x - 1} \right)\left( {x - 4} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
7x - 1 = 0\\
x - 4 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
7x = 1\\
x = 4
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{1}{7}\\
x = 4
\end{array} \right.\\
\Rightarrow S = \left\{ {\dfrac{1}{7};4} \right\}\\
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\
b)\left( {{x^2} - 4x} \right) - 5x + 20 = 0\\
\Leftrightarrow x\left( {x - 4} \right) - \left( {5x - 20} \right) = 0\\
\Leftrightarrow x\left( {x - 4} \right) - 5\left( {x - 4} \right) = 0\\
\Leftrightarrow \left( {x - 5} \right)\left( {x - 4} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 5 = 0\\
x - 4 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 5\\
x = 4
\end{array} \right.\\
\Rightarrow S = \left\{ {5;4} \right\}\\
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\
c){x^3} - 3{x^2} + x - 3 = 0\\
\Leftrightarrow \left( {{x^3} - 3{x^2}} \right) + \left( {x - 3} \right) = 0\\
\Leftrightarrow {x^2}\left( {x - 3} \right) + \left( {x - 3} \right) = 0\\
\Leftrightarrow \left( {{x^2} + 1} \right)\left( {x - 3} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
{x^2} + 1 = 0\\
x - 3 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
{x^2} = - 1\left( {vô\,\,lý} \right)\\
x = 3
\end{array} \right.\\
\Rightarrow S = \left\{ 3 \right\}\\
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\
d){x^3} - 2{x^2} - 9x + 18 = 0\\
\Leftrightarrow \left( {{x^3} - 2{x^2}} \right) - \left( {9x - 18} \right) = 0\\
\Leftrightarrow {x^2}\left( {x - 2} \right) - 9\left( {x - 2} \right) = 0\\
\Leftrightarrow \left( {{x^2} - 9} \right)\left( {x - 2} \right) = 0\\
\Leftrightarrow \left( {x - 3} \right)\left( {x + 3} \right)\left( {x - 2} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 3 = 0\\
x + 3 = 0\\
x - 2 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 3\\
x = - 3\\
x = 2
\end{array} \right.\\
\Rightarrow S = \left\{ {3; - 3;2} \right\}
\end{array}\]
Hãy giúp mọi người biết câu trả lời này thế nào?
Giải thích các bước giải:
`a)` `7x(x-4)-x+4=0`
`↔7x(x-4)-(x-4)=0`
`↔(7x-1)(x-4)=0`
`↔` \(\left[ \begin{array}{l}7x-1=0\\x-4=0\end{array} \right.\)`↔` \(\left[ \begin{array}{l}x=\dfrac{1}{7}\\x=4\end{array} \right.\)
Vậy `x in {1/7 ;4}`
`b)` `(x^2 -4x)-5x+20=0`
`↔[x(x-4)]-(5x-20)=0`
`↔x(x-4)-5(x-4)=0`
`↔(x-5)(x-4)=0`
`↔` \(\left[ \begin{array}{l}x-5=0\\x-4=0\end{array} \right.\)`↔` \(\left[ \begin{array}{l}x=5\\x=4\end{array} \right.\)
Vậy `x in {5;4}`
`c)` `x^3 -3x^2 +x-3=0`
`↔x^2 (x-3)+(x-3)=0`
`↔(x^2 +1)(x-3)=0`
`↔` \(\left[ \begin{array}{l}x^2 +1=0\\x-3=0\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}\ x^2 =-1(\text{vô lí vì}:x^2 \geqslant 0 \ \text{với mọi x})\\x=3\end{array} \right.\)
Vậy `x=3`
`d)` `x^3 -2x^2 -9x+18=0`
`↔(x^3 -2x^2)-(9x-18)=0`
`↔x^2 (x-2)-9(x-2)=0`
`↔(x^2 -9)(x-2)=0`
`↔(x^2 -3^2)(x-2)=0`
`↔(x-3)(x+3)(x-2)=0`
`↔` \(\left[ \begin{array}{l}x-3=0\\x+3=0\\x-2=0\end{array} \right.\)`↔` \(\left[ \begin{array}{l}x=3\\x=-3\\x=2\end{array} \right.\)
Vậy `x in {3;-3;2}`
Hãy giúp mọi người biết câu trả lời này thế nào?
Bảng tin