解：∵各项都为正数的数列{a[n]}，满足a[1]=1，a[n+1]^2-a[n]^2=2∴{a[n]^2}是首项为a[1]^2=1，公差为2的等差数列即：a[n]^2=1+2(n-1)=2n-1∴a[n]=√(2n-1)
