Question

一道初二奥数题，请高手马上给我解答，感激不尽！！！

1+（2010的平方）+（2010的平方除以2011的平方），这个结果开根号，然后再减去（1除以2011）

Answer 1

令a=2011
则2010=a-1
原式=√[1+(a-1)²+(a-1)²/a²]-1/a
=√{[(a²+a²(a-1)²+(a-1)²]/a²}-1/a

单独算a²+a²(a-1)²+(a-1)²
=(a-1)²-2a(a-1)+a²+2a(a-1)+a²(a-1)²
=(a-1)-a]²+2a(a-1)+a²(a-1)²
=1+2a(a-1)+a²(a-1)²
=[1+a(a-1)]²
所以原式=√{[1+a(a-1)]²/a²}-1/a
=[1+a(a-1)]/a-1/a
=[1+a(a-1)-1]/a
=a(a-1)/a
=a-1
=2010
应该蛮详细了

Answer 2

令a=2011
则2010=a-1
原式=√[1+(a-1)²+(a-1)²/a²]-1/a
=√{[(a²+a²(a-1)²+(a-1)²]/a²}-1/a

单独算a²+a²(a-1)²+(a-1)²
=(a-1)²-2a(a-1)+a²+2a(a-1)+a²(a-1)²
=(a-1)-a]²+2a(a-1)+a²(a-1)²
=1+2a(a-1)+a²(a-1)²
=[1+a(a-1)]²
所以原式=√{[1+a(a-1)]²/a²}-1/a
=[1+a(a-1)]/a-1/a
=[1+a(a-1)-1]/a
=a(a-1)/a
=a-1
=2010

Answer 3

这么简单自己做吧
加油