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1. <=> \(\left(3x+2\right)^3-\left(\left(3x\right)^3+2^3\right)=0\)
<=> \(\left(\left(3x\right)^3+2^3+3\left(3x+2\right).3x.2\right)-\left(\left(3x\right)^3+2^3\right)=0\)
<=>3 (3x + 2) . 3x.2 = 0
<=> (3x + 2 ) . x = 0
<=> x = -2/3 hoặc x = 0
2. Tương tự
1
\(\left(3x+2\right)^3-\left[\left(3x\right)^3+2^3\right]=0\)
\(\left(3x\right)^3+3\cdot\left(3x\right)^2\cdot2+3\cdot3x\cdot2^2+2^3-\left(3x\right)^3-2^3=0\)
\(54x^2+36x=0\)
\(18x\left(3x+2\right)=0\)
\(\orbr{\begin{cases}x=0\\3x+2=0\end{cases}}\)
\(\orbr{\begin{cases}x=0\\x=\frac{-2}{3}\end{cases}}\)
2
\(\left(2x+1\right)^3-\left[\left(2x\right)^3-1^3\right]=0\)
\(\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2+1^3-\left(2x\right)^3-1^3=0\)
\(12x^2+6x=0\)
\(6x\left(2x+1\right)=0\)
\(\orbr{\begin{cases}x=0\\2x+1=0\end{cases}}\)
\(\orbr{\begin{cases}x=0\\x=\frac{-1}{2}\end{cases}}\)
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mk giải từng nha == tại vì mk sợ nhiều qus bị troll
\(\left(3x-2\right)\left(9x^2+6x+4\right)-\left(3x-1\right)\left(9x^2-3x+1\right)=x-4\)
\(27x^3+18x^2+12x-18x^2-12x-8-3x\left(9x^2-3x+1\right)+\left(9x^2-3x+1\right)=x-4\)
\(27x^3-8-3\left(9x^2-3x+1\right)+9x^2-3x+1=x-4\)
\(27x^3-7-3x\left(9x^2-3x+1\right)+9x^2-3x=x-4\)
\(27x^3-7-27x^3+9x^2-3x+9x^2-3x=x-4\)
\(-7+18x^2-6x=x-4\)
\(3-18x^2+7x=0\)
\(x=\frac{-7+\sqrt{265}}{-36};\frac{-7-\sqrt{265}}{-36}\)
\(9\left(2x+1\right)=4\left(x-5\right)^2\)
\(18x+9=4x^2-40x+100\)
\(18x+9-4x^2+40x-100=0\)
\(58x-91-4x^2=0\)
\(x=\frac{29-3\sqrt{53}}{4};\frac{29+3\sqrt{53}}{4}\)
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Câu hỏi của Trịnh Minh Châu - Toán lớp 8 - Học toán với OnlineMath
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a) \(x^2+4x+3\)
\(=x^2+3x+x+3\)
\(=x\left(x+3\right)+\left(x+3\right)\)
\(=\left(x+1\right)\left(x+3\right)\)
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\(x^4+x^3+3x^2+2x+2=0\)
\(\Leftrightarrow x^4-x^3+x^2+2x^2-2x+2\)
\(\Leftrightarrow x^2\left(x^2-x+1\right)+2\left(x^2-x+1\right)\)
\(\Leftrightarrow\left(x^2+2\right)\left(x^2-x+1\right)\)
\(\Leftrightarrow\left(x^2+2\right)\left(x^2-x+\frac{1}{4}+\frac{3}{4}\right)\)
\(\Leftrightarrow\left(x^2+2\right)\left[x-\frac{1}{2}^2\right]+\frac{3}{4}\)
Ta co: \(\left(x-\frac{1}{2}\right)^2+\frac{3}{4}>\frac{3}{4}\)
\(\left(x^2+2\right)\left[\left(x-\frac{1}{2}^2\right)+\frac{3}{4}\right]\ge\frac{3}{2}\le0\)
đây sao nó cứ giống giống vs bài lớp 6 thì đúng hơn á
(x - 3)2 - 4 = 0
=> (x - 3 - 2)(x - 3 + 2) = 0
=> (x - 5)(x - 1) = 0
=> \(\orbr{\begin{cases}x-5=0\\x-1=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=5\\x=1\end{cases}}\)
(x + 2)2 - 9 = 0
=> (x + 2 - 3)(x + 2 + 3) = 0
=> (x - 1)(x + 5) = 0
=> \(\orbr{\begin{cases}x-1=0\\x+5=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=1\\x=-5\end{cases}}\)