Question

Alguem sabe responder??
2x²-12x+7=0

Answer 1

Olá

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calculando o delta

$\triangle=b^2-4\cdot a\cdot c$

a=2 ;   b=-12;    c=7;

$\triangle=(-12)^2-4\cdot 2\cdot 7 \\ \\ \triangle=144-56 \\ \\ \triangle= 88$


Calculando as raízes

$\displaystyle X= \frac{-b \pm \sqrt{\triangle} }{2\cdot a} \\ \\ \\ X_1= \frac{-12\pm \sqrt{88} }{2\cdot 2} ~~~~~~~~~~~~~\text{racionaliza a raiz} \\ \\ X_1= \frac{12+2 \sqrt{22} }{4}~~~~~ ~~~~ ~~~~~ \text{poe o 2 em evidencia} \\ \\ X_1= \frac{\diagup\!\!\!\!2(6+ \sqrt{22} )}{\diagup\!\!\!\!\!4} ~~~~~~~~~~~~\text{simplifica} \\ \\ \\ \boxed{X_1= \frac{6+ \sqrt{22} }{2} }~~~~~~~~\longleftarrow \text{Esta e a primeira raiz}$

$\displaystyle X_2= \frac{12-2 \sqrt{22} }{4}~~~~~ ~~~~ ~~~~~ \text{poe o 2 em evidencia} \\ \\ X_2= \frac{\diagup\!\!\!\!2(6- \sqrt{22} )}{\diagup\!\!\!\!\!4} ~~~~~~~~~~~~\text{simplifica} \\ \\ \\ \boxed{X_2= \frac{6- \sqrt{22} }{2} }~~~~~~~~\longleftarrow \text{Esta e a segunda raiz}$