已知：(10a+b)(10c+d)=(10a+c)(10b+d)=1000a+100b+10c+d,求a.b.c.d.

(10a+b)(10c+d)=(10a+c)(10b+d)推出d=100a
(10a+b)(10c+d)=100ac+10ad+10bc+bd代入d=100a得
(10a+b)(10c+d)=100ac+1000a*a+10bc+100ab=1000a*a+100(ac+ab)+10bc
题目中
(10a+b)(10c+d)=1000a+100b+10c+d=1000a+100b+10c+100a=1000a+100(a+b)+10c与上式比较,得a=1,b=1,c=1,d=100,验证正确