一个数学完全平方问题
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2.\u5947\u6570\u53ef\u5199\u4e3a10n+1\u300110n+3\u300110n+5\u300110n+7\u3001\u621610n+9\u4e94\u79cd\u5f62\u5f0f\u4e4b\u4e00\uff0c\u5c06\u5176\u5e73\u65b9\uff1a
(10n+1)^2=100n^2+20n+1=20n(5n+1)+1
(10n+3)^2=100n^2+60n+9=20n(5n+3)+9
(10n+5)^2=100n^2+100n+25=20n(5n+5)+25
(10n+7)^2=100n^2+140n+49=20n(5n+7)+49
(10n+9)^2=100n^2+180n+81=20n+(5n+9)+81
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3.\u4e00\u4e2a\u5e73\u65b9\u6570\u7684\u4e2a\u4f4d\u53ea\u4e0e\u539f\u6570\u7684\u4e2a\u4f4d\u6709\u5173\uff0c\u5217\u51fa\u4e2a\u4e2a\u4f4d\u6570\u7684\u5e73\u65b9\u6570\uff1a
1^2=1 2^2=4 3^2=9 4^2=16 5^2=25
6^2=36 7^2=49 8^2=64 9^2=81 0^2=0
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\uff0810n+4\uff09^2=100n^2+80n+16=20(5n^2+4n)+16
(10n+6)^2=100n^2+120n+36=20(5n^2+6n+1)+16
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\uff083m\uff09^2=9m^2
(3m+1)^2=9m^2+6m+1=3(3m^2+2m)+1
(3m+2)^2=9m^2+12m+4=3(3m^2+4m+1)+1
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\uff084m\uff09^2=16m^2
(4m+1)^2=16m^2+8m+1=4(4m^2+2m)+1
(4m+2)^2=16m^2+16m+4=4(4m^2+4m+1)
(4m+3)^2=16m^2+24m+9=4(4m^2+6m+2)+1
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\uff085m\uff09^2=25m^2
(5m+1)^2=25m^2+10m+1=5(5m^2+2)+1
(5m+2)^2=25m^2+20m+4=5(5m^2+4m)+4
(5m+3)^2=25m^2+30m+9=5(5m^2+6+1)+4
(5m+4)^2=25m^2+40m+16=5(5m^2+8+3)+1
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\uff088m\uff09^2=64m^2
(8m+1)^2=64m^2+16m+1=8(8m^2+2m)+1
(8m+2)^2=64m^2+32m+4=8(8m^2+4m)+4
(8m+3)^2=64m^2+48m+9=8(8m^2+6m+1)+1
(8m+4)^2=64m^2+64m+16=8(8m^2+8m+2)
(8m+5)^2=64m^2+80m+25=8(8m^2+10m+3)+1
(8m+6)^2=64m^2+96m+36=8(8m^2+12m+4)+4
(8m+7)^2=64m^2+112m+49=8(8m^2+14m+6)+1
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\uff0810n+1\uff09^2=100n^2+20n+1=20(5n^2+n)
(10n+3)^2=100n^2+60n+9=20(5n^2+3n)+9
(10n+5)^2=100n^2+100n+25=20(5n^2+5n+1)+5
(10n+7)^2=100n^2+140n+49=20(5n^2+7n+2)+7
(10n+9)^2=100n^2+180n+81=20(5n^2+9n+4)+1
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(x+y)²=\uff08x-y\uff09²+4xy=36
\uff08x-y\uff09²+4\u00d73=36
\uff08x-y\uff09²=24
x-y=\u00b1\u221a24
主要看根号里的数和它的倍数就可以了，一般都是配成完全平方式
主要还是化到不能化为止
首先配成完全平方式，例如(A+B)的N次方根然后化简就行了
配成完全平方式，一般方法：根号里还有根号的那一项就不动它了，拆其他的项，凑出完全平方式。这类题属简单题，不会考很多，放心.希望对你有帮助...
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