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a) 5x + 10x2 - 3x2 - 54x = 0
\(\Rightarrow\) 7x2 - 49x = 0
\(\Leftrightarrow\) 7x( x - 7 ) = 0
\(\Leftrightarrow\left\{{}\begin{matrix}7x=0\\x-7=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=0\\x=7\end{matrix}\right.\)
Vậy ....
b) x2 + 5x + 6 - x2 - 3x - 10 = 0
\(\Leftrightarrow\) 2x - 4 = 0
\(\Leftrightarrow\) 2x = 4
\(\Leftrightarrow\) x = 2
Vậy .....
a) 5x(1-2x) - 3x(x+18) = 0
\(\Leftrightarrow5x-10x^2-3x^2-54x=0\)
\(\Leftrightarrow-13x^2-49x=0\)
\(\Leftrightarrow-x\left(13x+49\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-x=0\\13x+49=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\frac{-49}{13}\end{matrix}\right.\)
Vậy phương trình có tập nghiệm \(S=\left\{0;\frac{-49}{13}\right\}\)
b) \(\left(x+2\right)\left(x+3\right)-\left(x-2\right)\left(x+5\right)=0\)
\(\Leftrightarrow x^2+5x+6-\left(x^2+3x-10\right)=0\)
\(\Leftrightarrow2x+16=0\)
\(\Leftrightarrow x=-8\)
Vậy phương trình có nghiệm x = -8
c) \(\left(2x+3\right)\left(x-4\right)+\left(x-5\right)\left(x-2\right)=\left(3x-5\right)\left(x-4\right)\)
\(\Leftrightarrow2x^2-8x+3x-12+x^2-2x-5x+10=3x^2-12x-5x+20\)
\(\Leftrightarrow3x^2-12x-2=3x^2-17x+20\)
\(\Leftrightarrow3x^2-3x^2-12x+17x-2-20=0\)
\(\Leftrightarrow5x-22=0\)
\(\Leftrightarrow x=\frac{22}{5}=4,4\)
Vậy phương trình có nghiệm x = 4,4.
c) 2x2 - 11x - 12 + x2 - 7x + 10 = 3x2 - 17x + 20
\(\Rightarrow\) 2x2 + x2 - 3x2 - 11x - 7x + 17x - 12 + 10 - 20 = 0
\(\Leftrightarrow\) -x - 22 = 0
\(\Leftrightarrow\) -x = 22
\(\Leftrightarrow\) x = -22
Vậy .....
