Let A abcd be a four-digit number.If 400abcd is a square of an integer ,then A=____or_____这道题答案是4001或8004,(注:four-digit 四位数;square 平方、平方数;integer 整数)
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Let A abcd be a four-digit number.If 400abcd is a square of an integer ,then A=____or_____
这道题答案是4001或8004,
(注:four-digit 四位数;square 平方、平方数;integer 整数)
4000000+A=n^2
A=n^2-2000^2=(n+2000)(n-2000)
因为A是4位数,且n+2000>2000所以0
经试验,后两解舍去
n=2001,A=4001
n=2002,A=8004
400abcd 显然是整数200a的平方,由于2003的平方4012009,已经大于400abcd,所以400abcd只能是2001或者2002的平方,2001的平方等于4004001,末四位4001是四位数,满足条件,2002的平方等于4008004,末四位8004也是四位数,也满足条件,所以A=4001 or 8004
Let A abcd be a four-digit number.If 400abcd is a square of an integer ,then A=____or_____
∵
1000
sqrt(4009999)≈ 2002.50
∴400abcd 只能是2001,2002的平方
对应的abcd 是 2001^2-4000000 = 4001
2002^2-4000000 = 8004
Let A abcd be a four-digit number.If 400abcd is a square of an integer ,then A=____or_____这道题答案是4001或8004,(注:four-digit 四位数;square 平方、平方数;integer 整数)
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