A rectangle has length p cm, width q cm; p,q are integers. If p,q satisfy the equation pq+p=p^2+13. Find the maximum of the area of the rectangle
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(x-1)(x2+3x-2)-(x3-1)=0
<=>(x-1)(x2+3x-2)-(x-1)(x2+x+1)=0
<=>(x-1)(x2+3x-2-(x2+x+1))=0
<=>(x-1)(x2+3x-2-x2-x-1)=0
<=>(x-1)(2x-3)=0
<=>x-1=0 hay 2x-3=0
<=>x=1 hay x=\(\frac{3}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
- <=>(x-1)(x2+3x-2) - (x-1)(x2+x+1)=0
- <=>(x-1)(x2+3x-2-x2-x-1)=0
- <=>(x-1)(2x-3)=0
- <=>x-1=0 hoặc 2x-3=0
- <=>x=1 hoặc x=3/2
VẬY S=1;3/2 :)))))))))))))))))))))))))
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\(\frac{x-2}{2012}+\frac{x-3}{2011}+\frac{x-4}{2010}+\frac{x-2029}{5}=0\)
\(\Leftrightarrow\frac{x-2}{2012}-1+\frac{x-3}{2011}-1+\frac{x-4}{2010}-1+\frac{x-2029}{5}+3=0\)
\(\Leftrightarrow\frac{x-2014}{2012}+\frac{x-2014}{2011}+\frac{x-2014}{2010}+\frac{x-2014}{5}=0\)
\(\Leftrightarrow\left(x-2014\right)\left(\frac{1}{2012}+\frac{1}{2011}+\frac{1}{2010}+\frac{1}{5}\right)=0\)
\(\Leftrightarrow x-2014=0\).Do \(\frac{1}{2012}+\frac{1}{2011}+\frac{1}{2010}+\frac{1}{5}\ne0\)
\(\Leftrightarrow x=2014\)
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\(\frac{y-1}{y-2}-\frac{5}{y+2}=\frac{12}{y^2-4}+1\)
\(\frac{\left(y-1\right)\left(y+2\right)}{y^2-4}-\frac{5\left(y-2\right)}{y^2-4}=\frac{12}{y^2-4}+\frac{y^2-4}{y^2-4}\)
\(\frac{y^2+y-2-5y+10}{y^2-4}=\frac{y^2+8}{y^2-4}\)
\(y^2-4y-8=y^2+8\)
\(y^2-4y-8-y^2-8=0\)
\(-4y-16=0\)
\(\Rightarrow y=-4\)
Vậy y=-4
\(\Leftrightarrow\frac{y-1}{y-2}-\frac{5}{y+2}=\frac{12}{\left(y-2\right)\left(y+2\right)}+1\)
\(\Leftrightarrow\frac{\left(y-1\right)\left(y+2\right)-5\left(y-2\right)-12+1\left(y-2\right)\left(y+2\right)}{\left(y-2\right)\left(y+2\right)}=0\)
\(\Leftrightarrow\frac{y^2+2y-y-2-5y+10-12+y^2+2y-2y-4}{\left(y-2\right)\left(y+2\right)}\)
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