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hoa [83]
3 years ago
11

What two numbers add to be 6 and multiply to be 15

Mathematics
1 answer:
yarga [219]3 years ago
4 0
   
\displaystyle \bf \\
x_1+x_2=6\\\\
x_1\cdot x_2=15\\\\
\Longrightarrow~~x^2-6x+15=0\\\\
x_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{6\pm\sqrt{36-60}}{2}=\\\\
=\frac{6\pm\sqrt{-24}}{2}=\frac{6\pm2\sqrt{-6} }{2}=3\pm i\sqrt{6}\\\\
x_1=\boxed{3-i\sqrt{6}}\\\\
x_2=\boxed{3+i\sqrt{6}}\\\\
\texttt{Verify:}\\\\
x_1+x_2=3-\underline{i\sqrt{6}}+3+\underline{i\sqrt{6}}=3+3=6~~correct\\\\
x_1\cdot x_2=(3-i\sqrt{6})(3+i\sqrt{6})=3^2-(i\sqrt{6})^2=9+6=15~~correct



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