Question

Resolva a equação |x|² - 10|x| + 21 = 0

Answer 1

Explicação passo-a-passo:

$\sf |x^2|-10|x|+21=0$

Seja $\sf |x|=y$

$\sf y^2-10y+21=0$

$\sf \Delta=(-10)^2-4\cdot1\cdot21$

$\sf \Delta=100-84$

$\sf \Delta=16$

$\sf y=\dfrac{-(-10)\pm\sqrt{16}}{2\cdot1}=\dfrac{10\pm4}{2}$

$\sf y'=\dfrac{10+4}{2}~\longrightarrow~y'=\dfrac{14}{2}~\longrightarrow~y'=7$

$\sf y"=\dfrac{10-4}{2}~\longrightarrow~y"=\dfrac{6}{2}~\longrightarrow~y"=3$

• Para $\sf y=7$:

$\sf |x|=7~\longrightarrow~x=7~oux=-7$

• Para $\sf y=3$:

$\sf |x|=3~\longrightarrow~x=3~oux=-3$

$\sf S=\{-7,-3,3,7\}$