Question

rezolvati in R ecuatia √x=x-2

Answer 1

Deoarece √x≥0=>x-2≥0=>x≥2.

Prin ridicare la patrat, obtinem:

$x=(x-2) ^{2} \ \textless \ =\ \textgreater \ x= x^{2} -4x+4\ \textless \ =\ \textgreater \ 0= x^{2} -5x+4\ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ 0= x^{2} -x-4x+4\ \textless \ =\ \textgreater \ 0=x(x-1)-4(x-1)\ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ 0=(x-1)(x-4)=\ \textgreater \ x=1~sau~x=4$

Dar 1<2, deci x=1 nu este solutie.

Singura solutie a ecuatiei este, deci, x=4.