Question

rezolvati ecuatiile√x+1=2;√x-3=x-3

Answer 1

$\sqrt{x+1}=2$
Conditii: x+1≥0 =>x∈[-1, ∞)
Ridicam la patrat:
x+1=4 =>x=3
S={3}
$\sqrt{x-3}=x-3$
Conditii : x-3≥0 =?x∈[3,∞)
Ridicam la patrat:
x-3=x²-6x+9 <=> x²-7x+12=0
Δ=b²-4ac=49-48=1 √Δ=1
x1=4 x2=3
S={3 ,4}