Toán a. (a+b-c)=12,b. (a+b-c)=15,c. (a+b-c)=8 13/09/2021 By Kylie a. (a+b-c)=12,b. (a+b-c)=15,c. (a+b-c)=8
\(\begin{array}{l} a\left( {a + b – c} \right) + b\left( {a + b – c} \right) – c\left( {a + b – c} \right) = 12 + 15 – 8\\ \Leftrightarrow \left( {a + b – c} \right)\left( {a + b – c} \right) = 19\\ \Leftrightarrow {\left( {a + b – c} \right)^2} = 19\\ \Rightarrow \left[ \begin{array}{l} a + b – c = \sqrt {19} \\ a + b – c = – \sqrt {19} \end{array} \right.\\ + )\,a + b – c = \sqrt {19} \Rightarrow a = \frac{{12}}{{\sqrt {19} }};b = \frac{{15}}{{\sqrt {19} }};c = \frac{8}{{\sqrt {19} }}\\ + )a + b – c = – \sqrt {19} \Rightarrow a = – \frac{{12}}{{\sqrt {19} }};b = – \frac{{15}}{{\sqrt {19} }};c = – \frac{8}{{\sqrt {19} }} \end{array}\) Trả lời
\(\begin{array}{l}
a\left( {a + b – c} \right) + b\left( {a + b – c} \right) – c\left( {a + b – c} \right) = 12 + 15 – 8\\
\Leftrightarrow \left( {a + b – c} \right)\left( {a + b – c} \right) = 19\\
\Leftrightarrow {\left( {a + b – c} \right)^2} = 19\\
\Rightarrow \left[ \begin{array}{l}
a + b – c = \sqrt {19} \\
a + b – c = – \sqrt {19}
\end{array} \right.\\
+ )\,a + b – c = \sqrt {19} \Rightarrow a = \frac{{12}}{{\sqrt {19} }};b = \frac{{15}}{{\sqrt {19} }};c = \frac{8}{{\sqrt {19} }}\\
+ )a + b – c = – \sqrt {19} \Rightarrow a = – \frac{{12}}{{\sqrt {19} }};b = – \frac{{15}}{{\sqrt {19} }};c = – \frac{8}{{\sqrt {19} }}
\end{array}\)