数学问题~~~高手请进

1.用杨辉三角形
a+b=1，a^2+b^2=2
ab=-1/2
(a+b)^3=a^3+3a^2b+3ab^2+b^3=a^3+b^3+3ab(a+b)=1
a^3+b^3=5/2
(a+b)^5=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5=1
a^5+b^5+5ab(a^3+b^3)+10a^2b^2(a+b)=1
a^5+b^5=1-5*(-1/2)(5/2)-10/4=19/4
(a+b)^7=a^7+7a^6b+21a^5b^2+35a^4b^3+35a^3b^4+21a^2b^5+7ab^6+b^7=1
a^7+b^7+7ab(a^5+b^5)+21a^2b^2(a^3+b^3)+35a^3b^3(a+b)=1
a^7+b^7=1-(-7/2)(19/4)-(21/4)(5/2)-(-35/8)=71/8
2.(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc=1
ab+ac+bc=-1/2
(a+b+c)^3=a^3+b^3+c^3+3(ab+ac+bc)(a+b+c)-3abc=1
abc=1/6
(a+b+c)^4=a^4+b^4+c^4+4a^3b+4a^3c+4b^3a+4b^3c+4c^3a+4c^3b
+6a^2b^2+6a^c^2+6b^2c^2+12a^2bc+12ab^2c+12abc^2=1
4(ab+ac+bc)(a^2+b^2+c^2)+3(a^2+b^2+c^2)(a^2+b^2+c^2)
+8(a+b+c)abc-2(a^4+b^4+c^4)=1
a^4+b^4+c^4=25/6