Question

$$\left. \begin{array} { l } { a b + a c = 71 , a + b + c = 2 } \\ { a c - b c = 40 } \end{array} \right.$$

Solve for a, b, c

$a=-\sqrt{70}i+1\approx 1-8.366600265i\text{, }b=-\sqrt{30}i+1\approx 1-5.477225575i\text{, }c=\left(\sqrt{30}+\sqrt{70}\right)i\approx 13.84382584i$
$a=-\frac{\left(\sqrt{30}-\sqrt{70}\right)\left(\sqrt{30}+\sqrt{70}+10\sqrt{21}i+70i\right)}{40}\approx 1+8.366600265i\text{, }b=-\frac{\left(\sqrt{30}-\sqrt{70}\right)\left(\sqrt{30}+\sqrt{70}+10\sqrt{21}i+30i\right)}{40}\approx 1+5.477225575i\text{, }c=\left(-\sqrt{30}-\sqrt{70}\right)i\approx -0-13.84382584i$
$a=-\frac{-\sqrt{70}i+10\sqrt{21}-70+\sqrt{30}i}{\sqrt{70}i-\sqrt{30}i}\approx 1-8.366600265i\text{, }b=-\frac{-\sqrt{70}i+10\sqrt{21}-30+\sqrt{30}i}{\sqrt{70}i-\sqrt{30}i}\approx 1+5.477225575i\text{, }c=\sqrt{70}i-\sqrt{30}i\approx 2.88937469i$
$a=-\frac{-\sqrt{30}i+10\sqrt{21}-70+\sqrt{70}i}{\sqrt{30}i-\sqrt{70}i}\approx 1+8.366600265i\text{, }b=-\frac{-\sqrt{30}i+10\sqrt{21}-30+\sqrt{70}i}{\sqrt{30}i-\sqrt{70}i}\approx 1-5.477225575i\text{, }c=\sqrt{30}i-\sqrt{70}i\approx -2.88937469i$