Question

Решите уравнение
√x-4 = √8-x

Answer 1

$\sqrt{T}=\sqrt{U}\ \ \textless \ -\ \textgreater \ \ \left \{ {{T=U} \atop {T \geq 0}} \right. \\\\ \sqrt{x-4}=\sqrt{8-x}\ \ \textless \ -\ \textgreater \ \ \left \{ {{x-4=8-x} \atop {x-4 \geq 0}} \right. \\\\ \left \{ {{2x=12} \atop {x \geq 4}} \right. \\\\ \left \{ {{x=6} \atop {x \geq 4}} \right. \\\\ x=6$

Answer 2

{x+8≥0⇒x≥-8
{x-4≥0⇒x≥4
x∈[4;∞)
(x-4)²=(√x+8)²
x²-8x+16=x+8
x²-9x+8=0
x1+x2=9 U x1*x2=8
x1=1 не удов усл
х2=8