Question

Fie S suma solutiilor reale ale ecuatiei lg²(2-x)-5lg(2-x)=0. S=?

Answer 1

lg²(2-x)-5lg(2-x)=0

C.E. 2-x>0=> x<2; x∈(-∞,2)

Notam y=lg(2-x)

y²-5y=0

y(y-5)=0

y1=0 => lg(2-x)=0; 2-x=1;

=> x1=1

y2=5 => lg(2-x)=5; 2-x=10^5;

=> x2=2-10^5

S=x1+x2=1+2-10^5

S=3-10^5