Question

Que valores de X satisfacen la educación 3χ²-4x+1=0

Answer 1

SOLUCIÓN

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                               $Sea\:la\:ecuaci\'on\:cuadr\'atica:\\\\\\ax^2+bx+c=0\\\\\\Por\:f\'ormula\:general\:tenemos\:que:\\\\\\\mathrm{\boxed{x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}}\\\\\\Del\:problema:\\\\\\a=1,b=-4,c=1\\\\\\ Entonces\:reemplazamos\\\\\\x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x_{1,2}=\dfrac{-(-4)\pm \sqrt{(-4)^2-[4(1)(1)]}}{2(1)}\\\\\\x_{1,2}=\dfrac{4\pm \sqrt{16-(4)}}{2}\\\\\\x_{1,2}=\dfrac{4\pm \sqrt{12}}{2}\\\\\\x_{1,2}=\dfrac{4\pm3.4641}{2}$

                             $\Rightarrow\:x_{1}=\dfrac{4+3.4641}{2}\\\\\\x_{1}=\dfrac{7.4641}{2}\\\\\\\boxed{\boldsymbol{x_{1}=3.73205}}\\\\\\\Rightarrow\:x_{2}=\dfrac{4-3.4641}{2}\\\\\\x_{2}=\dfrac{0.535898}{2}\\\\\\\boxed{\boldsymbol{x_{2}=0.267949}}$