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
Solution:
Given: $\left[(n+1)^{2}-n^{2}\right]=(n+1)+n$
(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) $(218)^{2}-(217)^{2}=218+217=435$