Question

determine o valor da raiz

√x2-12x+3=7

Answer 1

O resultado é:

$\sqrt{x^2}-12x+3=7\\\pm \:x-12x+3=7\\\pm \:x-12x=7-3\\\pm \:x-12x=4$
--------------------------------------------------
$x_1-12x_1=4\\-11x_1=4\\11x_1=-4\\\bold{x_1=-\frac{4}{11}}\text{ (Falso)}$
--------------------------------------------------
$-x_2-12x_2=4\\-13x_2=4\\13x_2=-4\\\bold{x_2=-\frac{4}{13}}\text{ (Verdadeiro)}$
--------------------------------------------------
Provando que $x_1$ é falso:

$\sqrt{\left(-\frac{4}{11}\right)^2}-12\left(-\frac{4}{11}\right)+3=7\\\\\left|-\dfrac{4}{11}\right|+\dfrac{12\cdot 4}{11}+3=7\\\\\dfrac{4}{11}+\dfrac{12\cdot 4}{11}=7-3\\\\\dfrac{4+\left(12\cdot 4\right)}{11}=4\\\\\dfrac{4\cdot \left(1+12\right)}{11}=4\\\\\dfrac{13}{11}=1\text{ (Falso)}$
--------------------------------------------------
Provando que $x_2$ é verdadeiro:

$\sqrt{\left(-\dfrac{4}{13}\right)^2}-12\left(-\dfrac{4}{13}\right)+3=7\\\\\left|-\dfrac{4}{13}\right|+\dfrac{12\cdot 4}{13}+3=7\\\\\dfrac{4}{13}+\dfrac{12\cdot 4}{13}=7-3\\\\\dfrac{4\cdot \left(1+12\right)}{13}=4\\\\\dfrac{13}{13}=1\\\\1=1\text{ (Verdadeiro)}$
--------------------------------------------------
$\boxed{\bold{\text{ Resposta: }S=\left\{x\in \mathbb{R},\:x=-\frac{4}{13}\right\}}}$