若a+b=5,ab=6,求a^2+b^2; a^4+b^4的值

显示全部楼层 · 2008-4-30 21:52:36

a+b=5(a+b)^2=a^2+2ab+b^2=25a^2+b^2=25-2ab=25-2*6=13a^2+b^2=13(a^2+b^2)^2=a^4+2a^2b^2+b^4=169a^4+b^4=169-2a^2b^2=169-2*(ab)^2=169-2*36=97

千问 · 2008-4-30 21:52:36

a^2+b^2=(a+b)^2-2ab=13a^4+b^4=(a^2+b^2)^2-2a^2b^2=97

千问 · 2008-4-30 21:52:36

a^2+b^2=(a+b)^2-2ab
=13a^4+b^4=(a^2+b^2)^2-2a^2b^2
=13^2-2*6^2
=97

千问 · 2008-4-30 21:52:36

a^2+b^2=(a+b)^2-2ab=13a^4+b^4=(a^2+b^2)^2-2(ab)^2=13^2-2*6^2=97;

千问 · 2008-4-30 21:52:36

a+b=5 (a+b)^2=a^2+2ab+b^2=25 a^2+b^2=25-2ab=25-2*6=13 a^2+b^2=13 (a^2+b^2)^2=a^4+2a^2b^2+b^4=169 a^4+b^4=169-2a^2b^2 =169-2*(ab)^2 =169-2*36 =97 z