Question

VA ROG AJUTOR!!!
Expresia este aceea de sus;trebuie sa aratam ca este x+1/x-1 ​

Answer 1

a) E(√2)=(√2+1)+1/(√2-1)=(√2+1)+(√2+1)=2√2+2
b)F(-√2)=(-√2-1)+1/(-√2+1)=(-√2-1)+1/(1-√2)=(-√2-1)+(1+√2)/(1-2)=
=-√2-1-(-1-√2)=-√2-1+1+√2=0
E(√2)≠F(-√2)
c) E(a)=a+1+1/(a-1)=[(a+1)(a-1)+1]/(a-1)=(a²-1+1)/(a-1)=a²/(a-1)
F(-a)=-a-1+1/(-a+1)=-a-1+1/(1-a)=[(-a-1)(1-a)+1}/(1-a)=(-a+a²-1+a+1)/(1-a)=
=a²/(1-a)
E(a)+F(-a)=a²/(a-1)+a²/(1-a)=(-a²+a²)/(1-a)=0
d) F(b)=b-1+1/(b+1)=[(b-1)(b+1)+1]/(b+1)=b²/(b+1)
E(b)=b+1+1/(b-1)=[(b+1)(b-1)+1]/(b-1)=b²(b-1)
F(b)/E(b)=b²/(b+1):b²(b-1)=b²/(b+1)·(b-1)/b²=(b-1)/(b+1)
b+1Ib-1
b+1Ib+1
b+1Ib+1-b+1
b+1I2
b+1∈D2
D2={1,2}
b+1=1⇒b=0
b+1=2⇒b=1
b∈(0,1)