Question

решить уравнение с модулем:|x^2-12|=-4x

Answer 1

Ix² - 12I = - 4x
$\left \{ {{ x^{2} -12 \geq 0} \atop { x^{2} -12=-4x}} \right.$
x² - 12 = -4x
x² + 4x - 12 = 0
D₁ = 4 + 12 = 16
x₁ = (-2+4) / 1 = 2      не удов. усл. x²-12≥0
x₂ = (-2 - 4) / 1 = -6
$\left \{ {{ x^{2} -12\ \textless \ 0} \atop {-( x^{2} -12)=-4x}} \right.$
- (x² -12) = -4x
-x² + 12 + 4x = 0
x² - 4x - 12 = 0
D₁ = 4 +12 = 16
x₁ = (2+4) /1 = 6    не удов. усл. x²-12 < 0
x₂ = (2-4) / 1 = -2
Ответ: -6; -2