Question

若2X+4Y=1比较X^+Y^与1/20的大小 ^代表平方

Answer 1

2X+4Y=1

Y=(1-2X)/4

X^2+Y^2=X^2+(1-2X)^2/16

=5X^2/4-X/4+1/16

=5(X^2-X/5+1/100)/4 +1/16 -1/80

=5(X-1/10)^2/4 + 1/20

当X=1/10,Y=1/5时 ,X^+Y^=1/20,

其他情况,X^+Y^>1/20