列出方程式，化簡，求解

1)a*a+b*b=c*c;

2)a+b+c=1000;

->2)a=1000-(b+c);

->get 3)[1000-(b+c)]^2+b^2=c^2; //replace 2) into 1)

-> 1000^2-2000*(b+c)+(b+c)^2+b^2=c^2;

->2*(b*b+b*c-1000*(b+c))=1000^2;

->(1000-b)*(b+c)=5*10^5=2^5*5^6=625*800; //do prime factor

find the only solution where1000-b=625 and b+c=800

which a=200,b=375,c=425

,so the answer is 31875000;

或用偷懶的方法:

送出一行答案，看正確答案