Question

sa se rezolve in r ecuatia x=6(sqrt(x-2)-1)

Answer 1

x=6√(x-2)-6

C.E. x≥2

x+6=6√(x-2)

x²+12x+36=36x-72

x²-24x+108=0

x1,2=(24+/-√144)/2= (24+/-12)/2

x1=6∈Domeniului,...verifica 6=6(2-1)

x2=18∈Domeniului...verifica 18=6(4-1)

Answer 2

Mai intai facem inmultirea cu paranteza si anume :

6sqrt(x-2)-6=x

6sqrt(x-2)=6+x

Ridicam totul la patrat si obtinem : 36(x-2)=(6+x)^2

36x-72=36+12x+x^2

x^2+12x-36x+36+72=0

x^2-24x+108=0 . ( ecuatie de gradul al doilea )

delta=b^2-4ac=(-24)^2-4*1*108=576- 432=144

deci x1=(-b+sqrtdelta)/2a=(24+12)/2=36/2=18

x2=(-b-sqrtdelta)/2a=(24-12)/2=12/2=6

x = { 6 , 18 }