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\(a,2x\left(x+5\right)=\left(x+3\right)^2+\left(x-1\right)^2+20\)
\(\Leftrightarrow2x^2+10x=x^2+6x+9+x^2-2x+1+20\)
\(\Leftrightarrow2x^2-x^2-x^2+10x-6x+2x=30\)
\(\Leftrightarrow6x=30\)
\(\Leftrightarrow x=5\)
\(b,\left(2x-2\right)^2=\left(x+1\right)^2+3\left(x-2\right)\left(x+5\right)\)
\(\Leftrightarrow4x^2-8x+4=x^2+2x+1+3\left(x^2+3x-10\right)\)
\(\Leftrightarrow4x^2-8x+4=x^2+2x+1+3x^2+9x-30\)
\(\Leftrightarrow4x^2-8x-x^2-3x^2-2x-9x=-33\)
\(\Leftrightarrow-19x=-33\)
\(\Leftrightarrow x=\frac{33}{19}\)
\(c,\left(x-1\right)^2+\left(x+3\right)^2=2\left(x-2\right)\left(x+1\right)+38\)
\(\Leftrightarrow x^2-2x+1+x^2+6x+9=2\left(x^2-x-2\right)+38\)
\(\Leftrightarrow6x=25\)
\(\Leftrightarrow x=\frac{25}{6}\)
\(\dfrac{3}{\left(x-1\right)\left(x-3\right)}+\dfrac{2}{\left(x-3\right)\left(x-1\right)}=\dfrac{1}{\left(x-2\right)\left(x-3\right)}\)( ĐKXĐ: \(x\ne1\); \(x\ne3\); \(x\ne2\))
\(\Leftrightarrow\dfrac{3+2}{\left(x-1\right)\left(x-3\right)}=\dfrac{1}{\left(x-3\right)\left(x-2\right)}\)
\(\Leftrightarrow\dfrac{5\left(x-2\right)}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}=\dfrac{x-1}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}\)
\(\Rightarrow5x-10=x-1\)
\(\Leftrightarrow5x-x=10-1\)
\(\Leftrightarrow4x=9\)
\(\Leftrightarrow x=\dfrac{9}{4}\)( thõa mãn ĐKXĐ)
Vậy phương trình có tập nghiệm S = \(\left\{\dfrac{9}{4}\right\}\)
\(\left(x-1\right)^2-1+x^2=\left(1-x\right)\left(x+3\right)\)
\(\Leftrightarrow\left(x-1\right)^2+\left(x-1\right)\left(x+1\right)=\left(1-x\right)\left(x+3\right)\)
\(\Leftrightarrow2x\left(x-1\right)=\left(1-x\right)\left(x+3\right)\)
\(\Leftrightarrow2x\left(x-1\right)+\left(x-1\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(3x+3\right)=0\)
\(\Rightarrow x=\pm1\)
Giúp tớ mấy câu còn lại đi các cậu, tớ cần gấp lắm ạ ;;-;;
\(\left(x-5\right)\left(x-1\right)=2x\left(x-1\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x-5-2x\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+5\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=-5\end{cases}}\)
Vậy............
\(5\left(x+3\right)\left(x-2\right)-3\left(x+5\right)\left(x+2\right)=0\)
\(\Leftrightarrow5\left(x^2+x-6\right)-3\left(x^2+7x+10\right)=0\)
\(\Leftrightarrow2x^2-16x-60=0\)
\(\Leftrightarrow x^2-8x-30=0\)
làm tiếp nhé!!!!!
a) \(\left(3x+2\right)^2-\left(3x-2\right)^2=5x+8\)
\(\Rightarrow\left(3x+2+3x-2\right)\left(3x+2-3x+2\right)=5x+8\)
\(\Rightarrow4.6x=5x+8\Rightarrow24x=5x+8\)
\(\Rightarrow19x=8\Rightarrow x=\frac{8}{19}\)
b) \(3\left(x-2\right)^2+9\left(x-1\right)=3\left(x^2+x-3\right)\)
\(\Rightarrow3\left(x^2-4x+4\right)+9x-9=3x^2+3x-9\)
\(\Rightarrow3x^2-12x+12+9x-9=3x^2+3x-9\)
\(\Rightarrow-12x+12+9x-9=3x-9\)
\(\Rightarrow-3x+3=3x-9\)
\(\Rightarrow6x=12\Rightarrow x=2\)
Nhân 2 vế với 2 rồi chuyển vế và rút gọn
Bạn Tên Là Long
a/ \(\Leftrightarrow2x^3+9x^2-27=0\)
\(\Leftrightarrow2x^3+12x^2+18x-3x^2-18x-27=0\)
\(\Leftrightarrow2x\left(x^2+6x+9\right)-3\left(x^2+6x+9\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(x+3\right)^2=0\)
\(\Leftrightarrow...\)
b/ \(\Leftrightarrow x^3-3x^2+3x-1+x^3+x^3+3x^2+3x+1=x^3+6x^2+12x+8\)
\(\Leftrightarrow x^3-3x^2-3x-4=0\)
\(\Leftrightarrow\left(x-4\right)\left(x^2+x+1\right)=0\)
c/ \(x\left(x+1\right)\left(x-1\right)\left(x+2\right)-24=0\)
\(\Leftrightarrow\left(x^2+x\right)\left(x^2+x-2\right)-24=0\)
Đặt \(x^2+x=t\)
\(t\left(t-2\right)-24=0\Leftrightarrow t^2-2t-24=0\Rightarrow\left[{}\begin{matrix}t=6\\t=-4\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x^2+x=6\\x^2+x=-4\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2+x-6=0\\x^2+x+4=0\end{matrix}\right.\)
d/ \(\Leftrightarrow\left(x-7\right)\left(x-2\right)\left(x-4\right)\left(x-5\right)-72=0\)
\(\Leftrightarrow\left(x^2-9x+14\right)\left(x^2-9x+20\right)-72=0\)
Đặt \(x^2-9x+14=0\)
\(t\left(t+6\right)-72=0\Leftrightarrow t^2+6t-72=0\Rightarrow\left[{}\begin{matrix}t=6\\t=-12\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x^2-9x+14=6\\x^2-9x+14=-12\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2-9x+8=0\\x^2-9x+26=0\end{matrix}\right.\)
( x3 + x3 + x3 ) + 13 + 23
= ( x3 + x3 + x3 ) + 33
=( x + 3 )3