Tìm x
( x –3 )³ – ( x – 3) . ( x² + 3x + 9) + 9 (x² + 1 ) = 63
Nhờ m.n giúp với a
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\(a,\left(x-3\right)\left(x-1\right)=\left(x-3\right)^2\\ \Leftrightarrow\left(x-3\right)\left(x-1-x+3\right)=0\\ \Leftrightarrow2\left(x-3\right)=0\\ \Leftrightarrow x=3\)
\(b,4x^2-9=0\\ \Leftrightarrow\left(2x-3\right)\left(2x+3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}2x-3=0\\2x+3=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{3}{2}\end{matrix}\right.\)
\(c,x^2+6x+9=0\\ \Leftrightarrow\left(x+3\right)^2=0\\ \Leftrightarrow x+3=0\\ \Leftrightarrow x=-3\)
a. \(\left(x-3\right)\left(x-1\right)=\left(x-3\right)^2\)
\(\Leftrightarrow\left(x-3\right)\left(x-1-x+3\right)=0\)
\(\Leftrightarrow2\left(x-3\right)=0\)
\(\Leftrightarrow x-3=0\)
\(\Leftrightarrow x=3\)
Bài 2:
\(\dfrac{1}{x}+\dfrac{1}{x+2}+\dfrac{x-2}{x\left(x+2\right)}\)
\(=\dfrac{x+x+2+x-2}{x\left(x+2\right)}=\dfrac{3x}{x\left(x+2\right)}=\dfrac{3}{x+2}\)
Để 3/x+2 là số nguyên thì \(x+2\in\left\{1;-1;3;-3\right\}\)
hay \(x\in\left\{-1;-3;1;-5\right\}\)
\(a,\left(3x+x\right)\left(x^2-9\right)-\left(x-3\right)\left(x^2+3x+9\right)\)
\(=4x\left(x^2-9\right)-x^3+27\)
\(=4x^3-36x-x^3+27\)
\(=3x^3-36x+27\)
\(\left(x+6\right)^2-2x.\left(x+6\right)+\left(x-6\right).\left(x+6\right)\)
\(=\left(x+6\right).\left(x+6-2x+x-6\right)\)
\(=\left(x+6\right).0\)
\(=0\)
câu a=219
câu b = 5 nha có 2 trường hợp xảy ra
câu c tương tự câu b nha bn
\(\Leftrightarrow\left(x-3\right)^3-\left(x-3\right)^3+9\left(x^2+1\right)=63\)
\(\Leftrightarrow9\left(x^2+1\right)=63\)
\(\Leftrightarrow x^2+1=7\)
\(\Leftrightarrow x^2=6\)
\(\Leftrightarrow x=\pm\sqrt{6}\)
ta có: ( x –3 )³ – ( x – 3) . ( x² + 3x + 9) + 9 (x² + 1 ) = 63
\(\Leftrightarrow x^3-3.x^2.3+3.x.3^2-3^3+3.\left(x^2+3x+9\right)-x\left(x^2+3x+9\right)+9x^2+\)\(9=63\)
\(\Leftrightarrow\left(x^3-x^3\right)-\left(9x^2-9x^2\right)+27x-\left(27-27\right)-\left(9x-9x\right)-\left(3x^2-3x^2\right)\)\(+9=63\)
\(\Leftrightarrow27x+9=63\)
\(\Leftrightarrow3x+1=7\)
\(\Leftrightarrow3x=6\)
\(\Leftrightarrow x=2\)
vậy: x=2