\(\left\{{}\begin{matrix}a+b=50\%\\a^2+b^2=14,5\%\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}a+b=\dfrac{1}{2}\\a^2+b^2=\dfrac{29}{200}\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}b=\dfrac{1}{2}-a\\a^2+\left(\dfrac{1}{2}-a\right)^2=\dfrac{29}{200}\end{matrix}\right.\)
\(\Leftrightarrow a^2+\dfrac{1}{4}-a+a^2=\dfrac{29}{200}\) \(\Leftrightarrow2a^2-a+\dfrac{21}{200}=0\)
\(\Delta=\left(-1\right)^2-4.2.\dfrac{21}{200}=1-\dfrac{21}{25}=\dfrac{4}{25}>0\)
\(\Rightarrow\) phương trình có 2 nghiệm phân biệt
\(a_1=\dfrac{1+\sqrt{\dfrac{4}{25}}}{4}=\dfrac{7}{20}\) \(\Rightarrow b=\dfrac{1}{2}-\dfrac{7}{20}=\dfrac{3}{20}\)
\(a_2=\dfrac{1-\sqrt{\dfrac{4}{25}}}{4}=\dfrac{3}{20}\) \(\Rightarrow b=\dfrac{1}{2}-\dfrac{3}{20}=\dfrac{7}{20}\)
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