Question

a=√8
b=$\frac{ \sqrt{2}+1 }{ \sqrt{2}-1 }$
a) verificati daca  [tex] \frac{a+2}{a-2} =b
[/tex]

Answer 1

A=√8=√2³=2√2
B=(√2+1)/(√2-1)=rationalizam=[(√2+1)(√2+1)]/[(√2-1)(√2+1)]=
   (√2+1)²/(2-1)=(√2+1)²=2+√2+√2+1=2√2+3
deci b=2√2+3

a)
(a+2)/(a-2)=b
(2√2+2)/(2√2-2)=2√2+3 rationalizam termenul din stanga
[(2√2+2)(2√2+2)]/[(2√2-2)(2√2+2)]=2√2+3
(2√2+2)²/(8-4)=2√2+3
(8+4√2+4√2+4)/4=2√2+3
(8√2+12)/4=2√2+3
4(2√2+3)/4=2√2+3
2√2+3=2√2+3