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Let a and b be the solutions to 5x^2 + 11x + 14 = 0. Find 1/a + 1/b

 Jan 17, 2021
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Let a and b be the solutions to 5x^2 + 11x + 14 = 0. Find 1/a + 1/b

 

Hello Guest!

 

\(5x^2 + 11x + 14 = 0\)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

\(x=\dfrac{-11\pm \sqrt{11^2-4\cdot 5\cdot 14}}{2\cdot 5}\)

\(a= -0.1i(\sqrt{159}+(-11i))\\ b= 0.1i(\sqrt{159}+11i)\)

\(\dfrac{1}{a}+\dfrac{1}{b}=1/(-0.1i(\sqrt{159}+(-11i)))+1/( 0.1i(\sqrt{159}+11i)) \)

\(\dfrac{1}{a}+\dfrac{1}{b}=-0.7\overline{857142}=-\dfrac{11}{14}\) 

laugh  !

 Jan 17, 2021
edited by asinus  Jan 17, 2021

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