Question

Rezolvati ecuatiile irationale :
1. $\sqrt{x^{2} -6x+25}=x+5$
2. $\sqrt{5x+1} - \sqrt{6x+7}=-1$
3. $\sqrt[3]{ x^{3}-4 x^{2} +6x+2 }=x-2$

Answer 1

1, CE
x²-6x+25>0 ,∀x∈R pt ca Δ=36-100<0
ramane ca x+5≥0, deci x≥-5

ridicam la patrat ambii membti
x²-6x+25=x²+10x+25
16x=0
x=0∈[-5;∞) solutia convine


2.
C.E.
(x≥-1/5)∩(x≥-7/6)=x≥-1/5
pt continuare, vezi attach

3
C.E. x∈R, radicalul fiind impar
 ridicam la puterea a treia fiecare membru
 x³-4x² +6x+2= x³-6x²+12x-8

-4x²+6x+2=-6x²+12x-8
-2x²+3x+1=-3x²+6x-4
x²-3x+5=0

Δ=9-20<0, x1,2∉R