设a,b,c满足a+b+c=1,a²+b²+c²=2,a³+b³+c³=3则abc=?

设a,b,c满足a+b+c=1,a²+b²+c²=2,a³+b³+c³=3则abc=?
设a,b,c满足a+b+c=1,a²+b²+c²=2,a³+b³+c³=3则abc=?

设a,b,c满足a+b+c=1,a²+b²+c²=2,a³+b³+c³=3则abc=?
根据a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-ac-bc)
=(a+b+c){a^2+b^2+c^2-(1/2)[(a+b+c)^2-(a^2+b^2+c^2)]}
=(a+b+c)[(3/2)(a^2+b^2+c^2)-(1/2)(a+b+c)^2]
=1x(3-1/2)
=5/2
所以abc=1/6