Using identities to find the values of the following:
1) 81^2-19^2
2) 275^2-225^2
3) 345^2-344^2
4) 538^2-462^2
5) 1001^2
6) 999^2
F.2 math easy identity plz help
2007-10-24 4:35 am
回答 (3)
2007-10-24 4:46 am
✔ 最佳答案
1)81^2-19^2
=(81+19)(81-19)
=100x62
=6200
2)
275^2-225^2
=(275+225)(275-225)
=500x50
=25000
3)
345^2-344^2
=(345+344)(345-344)
=689x1
=689
4)
538^2-462^2
=(538+462)(538-462)
=1000x76
=76000
5)
1001^2
=(1000+1)^2
=1000^2+2x1000x1+1^2
=1000000+2000+1
=1002001
6)
999^2
=(1000-1)^2
=1000^2-2x1000x1+1^2
=1000000-2000+1
=998001
2007-10-24 5:00 am
1) 81^2-19^2
=(81+19)(81-19)
=100x62
=6200
2) 275^2-225^2
=(275+225)(275-255)
=500x20
=10000
3) 345^2-344^2
=(345+344)(345-344)
=689x1
=689
4) 538^2-462^2
=(538+426)(538-426)
=964x112
=107968
5) 1001^2
=1001x1001
=1002001
6) 999^2
=999x999
=998001
=(81+19)(81-19)
=100x62
=6200
2) 275^2-225^2
=(275+225)(275-255)
=500x20
=10000
3) 345^2-344^2
=(345+344)(345-344)
=689x1
=689
4) 538^2-462^2
=(538+426)(538-426)
=964x112
=107968
5) 1001^2
=1001x1001
=1002001
6) 999^2
=999x999
=998001
參考: me
2007-10-24 4:47 am
1) 81^2 - 19^2 = (81+19)x(81-19) = 100x62 = 6200
2) 275^2 - 225^2 = (275+225)x(275-225) = 500x50 = 25000
3) 345^2 - 344^2 = (345+344)x(345-344) = 689x1 = 689
4) 538^2 - 462^2 = (538+462)x(538-462) = 1000x76 = 76000
5) 1001^2 = (1000+1)^2 = 1000^2 + 2x1000x1 + 1^2 = 1000000 + 2000 + 1 = 1002001
6) 999^2 = (1000-1)^2 = 1000^2 - 2x1000x1 + 1^2 = 1000000 - 2000 + 1 = 998001
RULES : a^2 - b^2 = (a+b)x(a-b)
(a+b)^2 = a^2 + 2ab + b^2
(a-b)^2 = a^2 - 2ab + b^2
2) 275^2 - 225^2 = (275+225)x(275-225) = 500x50 = 25000
3) 345^2 - 344^2 = (345+344)x(345-344) = 689x1 = 689
4) 538^2 - 462^2 = (538+462)x(538-462) = 1000x76 = 76000
5) 1001^2 = (1000+1)^2 = 1000^2 + 2x1000x1 + 1^2 = 1000000 + 2000 + 1 = 1002001
6) 999^2 = (1000-1)^2 = 1000^2 - 2x1000x1 + 1^2 = 1000000 - 2000 + 1 = 998001
RULES : a^2 - b^2 = (a+b)x(a-b)
(a+b)^2 = a^2 + 2ab + b^2
(a-b)^2 = a^2 - 2ab + b^2
參考: myself
收錄日期: 2021-04-13 14:07:21
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https://hk.answers.yahoo.com/question/index?qid=20071023000051KK03195