Question

quiero que me ayuden a resolver paso a paso este ejercicio!! (x- 3/2)² = 1/3 - 2/9

Answer 1

Quiero que me ayuden a resolver paso a paso este ejercicio!! (x- 3/2)² = 1/3 - 2/9 .

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$\textbf{Resolvemos:} \\ \\ \left(x- \dfrac{3}{2} \right)^{2} = \dfrac{1*3}{3*3} - \dfrac{2}{9} \\ \\ \\ x^{2}- \dfrac{6x}{2}+\dfrac{9}{4} = \dfrac{3}{9}-\dfrac{2}{9} \\ \\ \\ x^{2} -\dfrac{6x}{9}+\dfrac{9}{4} =\dfrac{1}{9}\\ \\ \\x^{2}-\dfrac{6x}{9}+ \dfrac{9}{4} -\dfrac{1}{9}\\ \\ \\ x^{2}-\dfrac{6x}{9}- \dfrac{77}{36} = 0 \\ \\ \\ Aplicamos\ la\ f\'ormula\ general: \\ \\ \boxed{ x_{1,2}= \frac{-b\ñ \sqrt{ b^{2}-4ac}}{2a}}$

$x_{1,2} =\dfrac{ -\left(-\dfrac{6}{9}\right)\ñ \sqrt{\left(- \dfrac{6}{9}\right)^{2} -\not{4}(1)\left( \dfrac{-77}{\not{36}} \right)}}{2(1)} \\ \\ \\ x_{1,2}=\dfrac{ \dfrac{6}{9}\ñ \sqrt{\dfrac{36}{81}+\dfrac{308}{9}}}{2} \\ \\ \\ x_{1,2}=\dfrac{ \dfrac{6}{9}\ñ \sqrt{\dfrac{104}{3}}}{2} \\ \\ Tenemos\ dos\ soluciones: \\ \\ \\ x_{1} = \dfrac{ \dfrac{6}{9} + \dfrac{ \sqrt{104} }{ \sqrt{3}}}{2} = \dfrac{ 6\sqrt{3}+18\sqrt{26} }{2} \\ \\ \\ x_{2} = \dfrac{6 \sqrt{3}- 18\sqrt{26} }{2}$