已知a+b=4,a^2+b^2=10,则a^4+b^4=

已知a+b=4,a^2+b^2=10,则a^4+b^4=
已知a+b=4,a^2+b^2=10,则a^4+b^4=

已知a+b=4,a^2+b^2=10,则a^4+b^4=
∵a+b=4
∴（a+b）^2=16
a^2+b^2+2ab=16
∵a^2+b^2=10
∴2ab=6
∴（2ab）^2=36,4a^2b^2=36,2a^2b^=18
∵(a^2+b^2)4=100
a^4+b^4+2a^2b^2=100
∴a^4+b^4=100-2a^2b^2
=100-18
=82