Question

若实数a平方+4b平方+c平方=1,则a+b+c的值最大值

Answer 1

a^2+4b^2+c^2=1,

因为2ab≤a^2+b^2,2bc≤b^2+c^2,2ca≤c^2+ a^2,

(a+b+c)^2

=a^2+b^2+c^2+2ab+2bc+2ca+3b^2-3b^2

=1+2ab+2bc+2ca-3b^2