1
Question
Evaluate:
(i) (38)2−(37)2
(ii) (75)2−(74)2
(iii) (92)2−(91)2
(iv) (105)2−(104)2
(v) (141)2−(140)2
(vi) (218)2−(217)2
Evaluate:
(i) (38)2−(37)2
(ii) (75)2−(74)2
(iii) (92)2−(91)2
(iv) (105)2−(104)2
(v) (141)2−(140)2
(vi) (218)2−(217)2
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Solution
We know that:
(n+1)2−n2=(n+1)+n
Therefore:
(i) (38)2−(37)2=38+37=75
(ii) (75)2−(74)2=75+74=149
(iii) (92)2−(91)2=92+91=183
(iv) (105)2−(104)2=105+104=209
(v) (141)2−(140)2=141+140=281
(vi) (218)2−(217)2=218+217=435
We know that:
(n+1)2−n2=(n+1)+n
Therefore:
(i) (38)2−(37)2=38+37=75
(ii) (75)2−(74)2=75+74=149
(iii) (92)2−(91)2=92+91=183
(iv) (105)2−(104)2=105+104=209
(v) (141)2−(140)2=141+140=281
(vi) (218)2−(217)2=218+217=435
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