第1个回答 2009-08-05
a^2+b^2=(a+b)^2-2ab=1-2ab=2 ab=-1/2
所以方程x^2-x-1/2=0的解为a,b
所以a^2=a+1/2 b^2=b+1/2
化简a^7=a(a^2)^3=a(a+1/2)^3=41/8a+15/8
同理化简b^7=41/8b+15/8
a^7+b^7=41/8(a+b)+15/8+15/8=71/8本回答被提问者采纳
第2个回答 2009-08-05
(a+b)^2=a^2+b^2-2ab
则ab=-1/2
代入a+b=1,得2a^2-2a-1=0
即 a^2=a+1/2,b^2=b+1/2
a^3=a*(a^2)=a^2+a/2 =3a/2 +1/2,b^3=b*(b^2)=b^2+b/2=3b/2 +1/2
a^4=a*(a^3)=a^3+a^2/2=2a+3/4,b^4=b*(b^3)=b^3+b^2/2=2b+3/4
所以a^7+b^7
= a^4*a^3+b^4*b^3
=(2a+3/4)(3a/2 +1/2)+(2b+3/4)(3b/2 +1/2)
=41a/8 +15/8 +41b/8+15/8
=41(a+b)/8 +30/8
=41/8 +30/8
=71/8
第3个回答 2009-08-05
已知a+b=1,a^2+b^2=2,求a^7+b^7的值
解:
a+b=1,a^2+b^2=2
(a+b)^2=a^2+b^2-2ab
1=2-2ab
ab=0.5
a^3+b^3=(a+b)^3-3ab(a+b)=1-3*0.5*1=-0.5
a^4+b^4=(a^2+b^2)^2-2(ab)^2=4-2*(0.5)^2=3.5
a^7+b^7
=(a^3+b^3)*(a^4+b^4)-(a^3b^4+a^4b^3)
=(-0.5)*3.5-(ab)^3*(a+b)
=-1.75-(0.5)^3*1
=-1.875
第4个回答 2009-08-05
由a+b=1,a^2+b^2=2可得a+b+a~2+b~2=3 两边配方得a~2+a+0.25+b~2+b+0.25=3.5
即(a+0.5)~2+(b+0.5)~2=3.5
然后在随便分一下,即使是无理数应该也没关系
就得出a b 的值 就能求出来