Question

[tranthuylinh]

\(xy=1100\)

\(y-\dfrac{1100}{x+5}=2\)

giải hpt

Answer 1

[missing you =]

\(\left\{{}\begin{matrix}xy=1100\\y-\dfrac{1100}{x+5}=2\end{matrix}\right.< =>\left\{{}\begin{matrix}y=\dfrac{1100}{x}\left(x\ne0\right)\left(1\right)\\\dfrac{1100}{x}-\dfrac{1100}{x+5}=2\left(2\right)\end{matrix}\right.\)

* giải pt(2)\(=>\dfrac{1100x+5500-1100x}{x^2+5x}=2\)

\(=>5500=2x^2+10x=>2x^2+10x-5500=0\)

\(=>\Delta=10^2-4\left(-5500\right)2=44100>0\)

\(=>\left[{}\begin{matrix}x1=\dfrac{-10+\sqrt{44100}}{2.2}=50\left(TM\right)\left(3\right)\\x2=\dfrac{-10-\sqrt{44100}}{2.2}=-55\left(TM\right)\left(4\right)\end{matrix}\right.\)

thế(3)(4) vào(1)\(=>\left[{}\begin{matrix}y=\dfrac{1100}{50}=22\\y=\dfrac{1100}{-55}=-20\end{matrix}\right.\)

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