请教高中数学题，急

1.(1)
Sn-1^2=a1^3+a2^3+a3^3+……+an-1^3 (1)
Sn^2=a1^3+a2^3+a3^3+……+an^3 (2)
(2)-(1)
(Sn+Sn-1)(Sn-Sn-1)=an^3
(Sn+Sn-an)an=an^3 (an>0)
(Sn+Sn-an)=an^2
2Sn-an=an^2

(2).
2Sn=an^2+an (1)
2Sn-1=an-1^2+an-1(2)
(1)-(2)
2an=an^2-an-1^2+an-an-1
0=an^2-an-1^2-an-an-1
0=(an-an-1)(an+an-1)-(an+an-1)
0=(an+an-1)(an + an-1 - 1)
因为an+an-1>0
所以an - an-1 = 1
数列{an}为公差为1的等差数列

S1=a1
S1^2=a1^3=a1^2 (a1>0)
所以解得a1=1
an=a1+(n-1)*1=n
数列{an}的通项公式 an=n

(3).
bn=3^n+入*2^(an)
bn=3^n+入*2^n (1)
bn+1=3^n+1+入*2^n+1
bn+1=3*3^n+2*入*2^n (2)
(2)-(1)
bn+1-bn=2*3^n+入*2^n>0
入>-2*3^n/2^n

则 入>2*(3/2)^n

2.
S=2x^2+2xy+y^2-4x+2y+1
S=x^2-4x+4+y^2+2y++1+x^2+2xy+y^2-4
S=(x-2)^2+(y+1)^2+(x+y)^2-4-y^2
讨论
(1) 当x-2=0 y+1=0 时 S=-4
(2) 当x-2=0 x+y=0 时 S=-7
(3)