Question

Aflati media aritmetica si media geometrica a numerelor.
$a=( \sqrt{n}+1)^{2}+( \sqrt{n}-1)^{2}$
$b=( \sqrt{n+1}+1)^{2} - ( \sqrt{n+1}-1 )^{2}$

Answer 1

a=(√n+1)²+(√n-1)²=n+2√n+1+n-2√n+1=2n+2=2(n+1)
b=(√(n+1)+1)²-(√(n+1)-1)²=n+1+2√(n+1)+1-n-1+2√(n+1)-1=4√(n+1)
(a+b)/2=[2n+2+4√(n+1)]/2=n+1+2√(n+1)
√(ab)=√(2(n+1)4√(n+1)=2√[2(n+1)√(n+1)]