1 证明
左边=(10x+y)[10x+(10-y)]
=100x^2+100x-10xy+10xy+10y-y^2
=100x^2+100x+10y-y^2
右边=100x^2+100x+10y-y^2
左边=右边
2 证明
a²+b²+c²-ab-bc-ca
1/2*2(a²+b²+c²-ab-bc-ca)
=1/2*(2a²+2b²+2c²-2ab-2bc-2ca)
=1/2*(a²-2ab+b²+b²-2bc+c²+a²-2ca+c²)
=1/2*(a-b)^2+(b-c)^2+(a-c)^2 =0
所以 a=bb=ca=c
又 a+b+c=1
即 a=b=c=1/3