Question

sa se rezolve, in multimea numerelor reale , ecuatia radical √x²-9+√x-3=0 .

Answer 1

x²-9≥0, (x-3)(x+3)≥0, x∈(-∞,-3]∪[3,+∞)
x-3≥0, x≥3, x∈[3,+∞)
x∈[3,+∞)
√x²-9=-√x-3
ridicam la patrat
x²-9=x-3
x²-x-6=0
Δ=1-4x1x(-6)=25
x1=(1+5)/2=3
x2=(1-5)/2=-2∉[3,+∞)
solutia este x=3