Question

$g) |x| ^ 2 - 3|x| = 10$ |x| 2 - 3|x| = 10

Answer 1

$\large\boxed{\begin{array}{l}\rm |x|^2-3|x|=10\\\rm fac_{\!\!,}a~|x|=y,com~y\geqslant0.\\\rm y^2-3y=10\\\rm y^2-3y-10=0\\\rm\Delta=b^2-4ac\\\rm\Delta=(-3)^2-4\cdot1\cdot(-10)\\\rm\Delta=9+40\\\rm\Delta=49\\\rm y=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\rm y=\dfrac{-(-3 )\pm\sqrt{49}}{2\cdot1}\\\\\rm y=\dfrac{3\pm7}{2}\begin{cases}\rm y_1=\dfrac{3+7}{2}=\dfrac{10}{2}=5\\\\\rm y_2=\dfrac{3-7}{2}=-\dfrac{4}{2}=-2\end{cases}\\\\\rm como~y\geqslant0,~temos~que~y=5\end{array}}$

$\large\boxed{\begin{array}{l}\rm como~|x|=y,podemos~escrever:\\\rm |x|=5\\\rm x=5~~ou~~x=-5\\\rm S=\{-5,5\}\end{array}}$