do sMiKAwvW dy vrgW iv`c sMbMD
( Relationship between the
squares of two Consecutive Numbers )
Students
Gurmukh Singh and Vicky Thakur of Govt. Model Sen.Sec.School P.A.U
Ludhiana establish a relationship
between two consecutive number in maths class.
According to
their observation, they find that square
of any number can also be obtained by adding squaring previous number with the
twice of given number and then subtracting one from the result .
srkwrI mwfl sInIAr
sYkMfrI skUl pI.ey.XU dy ividAwrQI gurmu`K isMG Aqy iv`kI TwkUr v`loN klws iv`c hI bYTy – bYTy do sMiKAwvW dy vrgW
iv`c sMbMD sQwipq krky AiDAwpkW nUM vI hYrwn kr id`qw [ auhnW ny d`isAw ik iksy
sMiKAw dw vrg aus qoN ipClI sMiKAw dy vrg iv`c sMiKAw dw dugxw joV ky Aqy AMq
iv`c ie`k Gtwaux qy vI iml jWdw hY [
audwhrx (Examples) :-
82 = 64 = 72
+ 2x8 -1 = 49 +16 -1
282 = 784 = 272 + 2x28 -1 = 729 +56 -1
ies dI puStI auhnW v`lo jnrl PwrmUlw lgw ky vI kIqI
geI hY[
They proved
it by applying general formula algebraically.
a2
= (a-1)2 +2a -1
= a2 + 1 -2a +2a -1 = a2