Question

sa se rezolve in R ecuatiile:
radical din x la a 2-4+radical din x-2=0

Answer 1

√x^2-4+√x-2=0
a=√x. b=-4+√1. c=-2 delta=b^2-4ac=(-4+√1)^2-4*√x*(-2)=3+8√x
x1=-b-√delta/2a=4+√1-√3+8√x/2*√x=4+√1-√3+8/2
x2=-b+√delta/2a=4+√1+√3+8√x/2*√x=4+√1+√3+8/2

Answer 2

$\sqrt {( x -2)(x+2)} + \sqrt{x-2} =0$
Punem conditii de existenta ale radicalilor
x²-4≥0 ⇒ x∈(-∞,-2]∪[+2,+∞)
x-2≥0 ⇒x≥2⇒x∈[+2,+∞)
Reunind intervalele ⇒x∈[+2,+∞)
$\sqrt {( x -2)}( \sqrt{x+2}+1) =0$
$\sqrt {( x -2)}=0 sau \sqrt{x+2}+1 =0$
$\sqrt {( x -2)}=0 , x=2$
$\sqrt{x+2}+1 =0 Nu are solutii reale$