Question

E(x)=/x-1/+/x+3/, x E R . a) aratati ca numarul E(radical din 2) este irational ,b) demonstrati ca E(x)=4 x E {-3,1} VA ROOGGG!!!!!

Answer 1

a) E (rad2)=|rad2 -1| + |rad2 +3|=rad2 -1+rad2 +3=2rad2 +2=2 (rad2 +1) € R-Q
b) x-1, x-1>=0, x>=1
|x-1|= 《
-x+1, x-1 <0, x<1

x+3, x+3>=0, x>=-3
|x+3|=《
-x-3, x+3<0, x <-3

pt x €[-3, 1] =>
E (x)= -x+1+x+3
E (x)= 4