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# help with algebra

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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!

$$5x^2 + 11x + 14 = 0$$

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

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

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

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

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

!

Jan 17, 2021
edited by asinus  Jan 17, 2021