Question

resuelve 12x2-17x+6=0

Answer 1

SOLUCIÓN

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                   $Sea\:la\:ecuaci\'on\:cuadr\'atica:\\\\ax^2+bx+c=0\\\\\\Por\:f\'ormula\:general\:tenemos\:que:\\\\\mathrm{\boxed{x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}}\\\\\\Del\:problema:\\\\a=12,b=-17,c=6\\\\\\ Entonces\:reemplazamos\\\\x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x_{1,2}=\dfrac{-(-17)\pm \sqrt{(-17)^2-[4(12)(6)]}}{2(12)}\\\\\\x_{1,2}=\dfrac{17\pm \sqrt{289-(288)}}{24}\\\\\\x_{1,2}=\dfrac{17\pm \sqrt{1}}{24}\\\\\\x_{1,2}=\dfrac{17\pm1}{24}$

                $\Rightarrow\:x_{1}=\dfrac{17+1}{24}\\\\\\x_{1}=\dfrac{18}{24}\\\\\\\boxed{\boldsymbol{x_{1}=0.75}}\\\\\\\Rightarrow\:x_{2}=\dfrac{17-1}{24}\\\\\\x_{2}=\dfrac{16}{24}\\\\\\\boxed{\boldsymbol{x_{2}=0.666667}}$