Cho tỉ lệ thức x+2y/22=x-2y/14. a) Tính tỉ số x/y. b) Tìm x, y biết x^2+y^2=82.

Đáp án:

$\begin{array}{l}a)\,\dfrac{x+2y}{22}=\dfrac{x-2y}{14}\\\Rightarrow 14.(x+2y)=22.(x-2y)\\\Rightarrow 14x+28y=22x-44y\\\Rightarrow 14x+28y+44y=22x\\\Rightarrow 28y+44y=22x-14x\\\Rightarrow y(28+44)=x(22-14)\\\Rightarrow 72y=8x\\\Rightarrow 72=\dfrac{8x}y\\\Rightarrow \dfrac{72}8=\dfrac xy\\\Rightarrow\dfrac xy=9\end{array}$

Vậy $\dfrac xy=9$.

$b)\,\dfrac xy=9\Rightarrow\dfrac x9=y=k\Rightarrow\left\{\begin{matrix}x=9k\\y=k\end{matrix}\right.\\\Rightarrow x^2+y^2=82\\\Rightarrow\left(9k\right)^2+k^2=82\\\Rightarrow 81k^2+k^2=82\\\Rightarrow 81k^2+k^2=82\\\Rightarrow k^2(81+1)=82\\\Rightarrow k^2.82=82\\\Rightarrow k^2=1\Rightarrow \left\{\begin{matrix}k=1\\k=-1\end{matrix}\right.\\\Rightarrow\left\{\begin{matrix}x=9k=9\\y=k=1\end{matrix}\right.\ \ \ \ \ {\rm{or}}\ \ \ \ \ \left\{\begin{matrix}x=9k=-9\\y=k=-1\end{matrix}\right.$

Vậy $x=9,y=1$ hoặc $x=-9,y=-1$.

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