Question

cit va fi radical din -x inmultit cu radical din 3-x=0

Answer 1

Pai radicalul tau exista <=> x<0 si daca 3-x >= 0, adica x mai mic sau egal decat 3. Intersectezi solutiile si rezulta x<0 Si va fi radical din(-x(3-x))=0 Rad.(xpatrat-3x)=0 Ridici la patrat sa scapi de radical si => xpatrat-3x=0 Scoti factor comun x(x-3)=0 => x1=0 si x2=3.

Answer 2

   
[tex] \sqrt{-x} \cdot \sqrt{3-x} =0 \\ \\ \sqrt{-x(3-x)} = 0 \\ \\ \sqrt{-3x+x^2} = 0 \\ \\ \sqrt{x^2-3x} = 0 ~~~ (Ridicam~la~puterea~a~doua)\\ \\ x^2-3x = 0 \\ \\ x(x-3) = 0 \\ \\ x = 0 ~~~\Longrightarrow~~~ \boxed{x_1 = 0} \\ \\ x - 3 = 0 ~~~\Longrightarrow~~~ \boxed{x_2 = 3} \\ \\ Verificari: \\ x_1 = 0 ~~~\Longrightarrow~~~ \sqrt{-0} \cdot \sqrt{3-0} = \sqrt{0} \cdot \sqrt{3} = 0 \cdot \sqrt{3} = 0 [/tex]

$x_2 = 3 ~~~\Longrightarrow~~~ \sqrt{-3} \cdot \sqrt{3-3} = i \sqrt{3} \cdot \sqrt{0} =i \sqrt{3} \cdot 0 = 0$