Tìm x:
3x^3-27x=0
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\(a\left(b^2-c^2\right)+b\left(c^2-a^2\right)+c\left(a^2-b^2\right)\)
\(=a\left(b^2-c^2\right)+b\left(c^2-b^2\right)+b\left(b^2-a^2\right)+c\left(a^2-b^2\right)\)
\(=\left(a-b\right)\left(b^2-c^2\right)+\left(c-b\right)\left(a^2-b^2\right)\)
\(=\left(a-b\right)\left(b-c\right)\left(b+c\right)+\left(c-b\right)\left(a-b\right)\left(a+b\right)\)
\(=\left(a-b\right)\left(b-c\right)\left(b+c-a-b\right)\)
\(=\left(a-b\right)\left(b-c\right)\left(c-a\right)\)
\(2x^2+y^2+2xy-8x-6y+10=0\)
\(\Rightarrow2.\left(2x^2+y^2+2xy-8x-6y+10\right)=0\)
\(\Rightarrow4x^2+2y^2+4xy-16x-12y+20=0\)
\(\Rightarrow\left(4x^2+y^2+16+4xy-8y-16x\right)+\left(y^2-4y+4\right)=0\)
\(\Rightarrow\left(2x+y-4\right)^2+\left(y-2\right)^2=0\left(1\right)\)
Ta có: \(\hept{\begin{cases}\left(2x+y-4\right)^2\ge0\forall x;y\\\left(y-2\right)^2\ge0\forall y\end{cases}\Rightarrow\left(2x+y-4\right)^2+\left(y-2\right)^2\ge0\forall x;y\left(2\right)}\)
Từ (1) và (2) \(\Rightarrow\hept{\begin{cases}2x+y-4=0\\y-2=0\end{cases}\Rightarrow\hept{\begin{cases}2x+y=4\\y=2\end{cases}\Rightarrow}\hept{\begin{cases}2x+2=4\\y=2\end{cases}\Rightarrow}\hept{\begin{cases}x=1\\y=2\end{cases}}}\)
Chúc bạn học tốt.
\(x^2-14x+13=0\)
\(\Rightarrow x^2-2x.7+7^2-7^2+13=0\)
\(\Rightarrow\left(x^2-2x.7+7^2\right)-7^2+13=0\)
\(\Rightarrow\left(x-7\right)^2-49+13=0\)
\(\Rightarrow\left(x-7\right)^2-36=0\)
\(\Rightarrow\left(x-7\right)^2=36\)
\(\Rightarrow\left(x-7\right)^2=\pm6^2\)
\(\Rightarrow\orbr{\begin{cases}x-7=6\\x-7=-6\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=13\\x=1\end{cases}}\)
Vậy ...
\(x^2-14x+13=0\)
\(x^2-14x+49-36=0\)
\(\left(x^2-14x+19\right)-36=0\)
\(\left(x-7\right)^2-6^2=0\)
\(\left(x-7-6\right)\left(x-7+6\right)=0\)
\(\left(x-13\right)\left(x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-13=0\\x-1=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=13\\x=1\end{cases}}\)
3x3 - 27 x = 0
=> 3x ( x2 - 9 ) = 0
\(=>\orbr{\begin{cases}3x=0\\x^2-9=0\end{cases}}\)
\(=>\orbr{\begin{cases}x=0\\x^2=9\end{cases}}\)
=> x = + 3
hoặc x = 0
\(3x^2-27x=0\)
\(\Leftrightarrow3x\left(x+3\right)\left(x-3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=\pm3\end{cases}}\)