(1)√11-2=3(2)√1111-22=33(3)√111111-222=333 √111…1(2n个1)-22…2(n个2)=?请加以证明
来源:学生作业帮助网 编辑:作业帮 时间:2024/11/14 21:17:19
(1)√11-2=3(2)√1111-22=33(3)√111111-222=333 √111…1(2n个1)-22…2(n个2)=?请加以证明
(1)√11-2=3(2)√1111-22=33(3)√111111-222=333 √111…1(2n个1)-22…2(n个2)=?
请加以证明
(1)√11-2=3(2)√1111-22=33(3)√111111-222=333 √111…1(2n个1)-22…2(n个2)=?请加以证明
2)√1111-22=√11(101-2)=√11*99=√(11*11*9)=33
3)√111111-222==√111(1001-2)=√(111*999)=√(111*111*9)=333
同理
√111…1(2n个1)-22…2(n个2)
=√{111……1(n个)*[1000……1-2]}
=√[111……1(n个)*999……9(n个)]
=√[111……1(n个)*111……1(n个)*9]
=33…3(n个3
√111…1(2n个1)-22…2(n个2)=33…3(n个3)
111...1(2n)-22...2(n)=111...1(2n)-2×111...1(n)=111...1(2n)-111...1(n)-111...1(n)
=111...1(n)000...0(n)-111...1(n)=111...1(n) × 1000...0(n) -111...1(n)
=111...1(n) ×{ 1000...0(n) -1}
=111...1(n) ×999...9(n)
=111...1(n) ×111...1(n) ×9 开根号 =333...3(n)