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\(\left(y-x+1\right)^2+\left(y+2\right)^2=0\\ \)
\(\Rightarrow\hept{\begin{cases}y=-2\\x=-1\end{cases}\Rightarrow\frac{3x^2y+1}{5xy}}=\frac{-6+1}{10}=-\frac{1}{2}\)
1) \(5xy^2\left(x-1\right)-3y\left(x^2-x\right)\)
\(=5xy^2\left(x-1\right)-3yx\left(x-1\right)\)
\(=\left(x-1\right)\left(5xy^2-3xy\right)\)
\(=xy\left(x-1\right)\left(5y-3\right)\)
\(1)\)\(5xy^2\left(x-1\right)-3y\left(x^2-x\right)\)
\(=\)\(5xy^2\left(x-1\right)-3xy\left(x-1\right)\)
\(=\)\(\left(x-1\right)\left(5xy^2-3xy\right)\)
\(=\)\(xy\left(x-1\right)\left(5y-3\right)\)
\(2)\)\(x\left(x-1\right)+y\left(x-1\right)+\left(x+y\right)^2\)
\(=\)\(\left(x-1\right)\left(x+y\right)+\left(x+y\right)^2\)
\(=\)\(\left(x+y\right)\left(x-1+x+y\right)\)
\(=\)\(\left(x+y\right)\left(2x+y-1\right)\)
\(3)\)\(x\left(x^2-2x\right)-2y\left(x^2-2x\right)+x-2y\)
\(=\)\(\left(x^2-2x\right)\left(x-2y\right)+\left(x-2y\right)\)
\(=\)\(\left(x-2y\right)\left(x^2-2x+1\right)\)
\(=\)\(\left(x-2y\right)\left(x-1\right)^2\)
Chúc bạn học tốt ~
2y² + 2x² = 5xy
<=> 2y² - 5xy + 2x² = 0
<=> (x - 2y)(2x - y) = 0
=> x = 2y hoặc y = 2x
Thay vào biểu thức ta có:
+) Nếu x = 2y => (x - y)/(x + y) = (2y - y)/(2y + y) = y/3y = 1/3
+) Nếu y = 2x => (x - y)/(x + y) = (x - 2x)/(x + 2x) = -x/3x = -1/3
1 ) \(x\left(a-b\right)+a-b=\left(x+1\right)\left(a-b\right)\)
2 ) \(2x\left(b-a\right)+a-b=2x\left(b-a\right)-\left(b-a\right)=\left(2x-1\right)\left(b-a\right)\)
3 ) \(-2x-2y+ax+ay=-2\left(x+y\right)+a\left(x+y\right)=\left(a-2\right)\left(x+y\right)\)
4 ) \(x^2-xy-2x+2y=x\left(x-y\right)-2\left(x-y\right)=\left(x-2\right)\left(x-y\right)\)
5 ) \(5x^2y+5xy^2+a^2x+a^2y\)
\(=5xy\left(x+y\right)+a^2\left(x+y\right)\)
\(=\left(5xy+a^2\right)\left(x+y\right)\)
6 ) \(2x^2-6xy+5x-15y\)
\(=2x\left(x-3y\right)+5\left(x-3y\right)\)
\(=\left(2x+5\right)\left(x-3y\right)\)
7 ) \(ax^2-3axy+bx-3by\)
\(=\left(ax^2+bx\right)-\left(3axy+3by\right)\)
\(=x\left(ax+b\right)-3y\left(ax+b\right)\)
\(=\left(x-3y\right)\left(ax+b\right)\)
8 ) \(x^2+4x-5x-20=0\)
\(\Leftrightarrow x\left(x+4\right)-5\left(x+4\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-4\end{matrix}\right.\)
9 ) \(x^2+10x-2x-20=0\)
\(\Leftrightarrow x\left(x+10\right)-2\left(x+10\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-10\end{matrix}\right.\)
10 ) \(x^2-6x-4x+24=0\)
\(\Leftrightarrow x\left(x-6\right)-4\left(x-6\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x-6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x-6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=6\end{matrix}\right.\)
:D