(x+y)^2=18,(x-y)^2=6,分别求x^2+y^2及x^2+3xy+y^2的值

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(x+y)^2=18,(x-y)^2=6,分别求x^2+y^2及x^2+3xy+y^2的值(x+y)^2=18,(x-y)^2=6,分别求x^2+y^2及x^2+3xy+y^2的值(x+y)^2=18

(x+y)^2=18,(x-y)^2=6,分别求x^2+y^2及x^2+3xy+y^2的值
(x+y)^2=18,(x-y)^2=6,分别求x^2+y^2及x^2+3xy+y^2的值

(x+y)^2=18,(x-y)^2=6,分别求x^2+y^2及x^2+3xy+y^2的值
(x+y)^2=18=x^2+y^2+2xy,(x-y)^2=x^2+y^2-2xy=6
得出xy=3
x^2+y^2=(x+y)^2-2xy=18-6=12
x^2+3xy+y^2==(x+y)^2+xy=18+3=21

x^2+y^2=12
x^2+3xy+y^2=21

x^2+y^2=[(x+y)^2+(x-y)^2]/2=(18+6)/2=12
x^2+3xy+y^2=(x+y)^2+xy=(x+y)^2+[(x+y)^2-(x-y)^2]/4=18+(18-6)/4=21