Question

求教数学题已知a+b=3,ab=1,a^4+b^4=?

已知a+b=3,ab=1,则a的4次方加b的4次方的值是?
求结果及详细过程。

Answer 1

a+b=3,ab=1
a^2+b^2=(a+b)^2-2ab=9-2=7
a^4+b^4
=(a^2+b^2)^2-2a^2b^2
=7^2-2*1
=49-2
=47

Answer 2

a+b=3,ab=1
a^2+b^2=(a+b)^2-2ab=9-2=7
a^4+b^4
=(a^2+b^2)^2-2a^2b^2
=7^2-2*1
=49-2
=47

Answer 3

a^2+b^2
=(a+b)^2-2ab
=3^2-2*1
=9-2
=7

a^4+b^4
=(a^2+b^2)^2-2(ab)^2
=7^2-2*1^2
=49-2
=47

Answer 4

a^4+b^4
=（a^2+b^2)^2-2a^2b^2
=[(a+b)^2-2ab]^2-2(ab)^2
=[3^2-2*1]^2-2*1
=49-2
=47

Answer 5

a^2+b^2=(a+b)^2-2ab=7
a^4+b^4=(a^2+b^2)^2-2a^2b^2
=49-2*1*1=47