\(\dfrac{360}{x}-\dfrac{400}{x+1}=1\) (ĐK: \(x\ne0,x\ne-1\))
\(\Leftrightarrow\dfrac{360\left(x+1\right)}{x\left(x+1\right)}-\dfrac{400x}{x\left(x+1\right)}=\dfrac{x\left(x+1\right)}{x\left(x+1\right)}\)
\(\Leftrightarrow360\left(x+1\right)-400x=x\left(x+1\right)\)
\(\Leftrightarrow360x+360-400x=x^2+x\)
\(\Leftrightarrow-40x+360=x^2+x\)
\(\Leftrightarrow x^2+40x+x-360=0\)
\(\Leftrightarrow x^2+41x-360=0\)
\(\Rightarrow\Delta=41^2-4\cdot1\cdot\left(-360\right)=3121>0\)
\(\Rightarrow\left[{}\begin{matrix}x_1=\dfrac{-41+\sqrt{3121}}{2\cdot1}\approx7\left(tm\right)\\x_2=\dfrac{-41-\sqrt{3121}}{2\cdot1}\approx-48\left(tm\right)\end{matrix}\right.\)
\(\dfrac{360}{x}-\dfrac{400}{x+1}=1\)
Điều kiện: \(x\ne0;x\ne-1\)
PT \(\Leftrightarrow\dfrac{360\left(x+1\right)-400x}{x\left(x+1\right)}=1\)
\(\Rightarrow-40x+360=x\left(x+1\right)\)
\(\Leftrightarrow-40x+360=x^2+x\)
\(\Leftrightarrow x^2+41x-360=0\)
\(\Leftrightarrow x^2+2.\dfrac{41}{2}.x+\dfrac{1681}{4}=\dfrac{3121}{4}\)
\(\Leftrightarrow\left(x+\dfrac{41}{2}\right)^2=\left(\dfrac{\sqrt{3121}}{2}\right)^2\)
\(\Leftrightarrow x+\dfrac{41}{2}=\dfrac{\sqrt{3121}}{2}\) hoặc \(x+\dfrac{41}{2}=-\dfrac{\sqrt{3121}}{2}\)
\(\Leftrightarrow x=\dfrac{\sqrt{3121}}{2}-\dfrac{41}{2}\) hoặc \(x=-\dfrac{\sqrt{3121}}{2}-\dfrac{41}{2}\)
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