1299 x 1299 = (1299)2
= (1300 - 1)2
= (1300)2 + (1)2 - 2 x 1300 x 1
= 1690000 + 1 - 2600 = 1687401
1307 x 1307 = (1307)2
= (1300 + 7 )2
= (1300)2 + (7)2 + 2 x 1300 x 7
= 1690000 + 49 +18200
= 1708249
5358 x 51 = 5358 x (50 +1 )
5358 x 50 + 5358 x 1
=267900 + 5358 = 273258
106 x 106 + 94 x 94 =(106)2 + (94)2
=1/2 [2(a2 + b2)]
=1/2 [(a+b)2 + (a-b)2]
=1/2 [(106 + 94)2 + (106 -94 )2]
=1/2 [ (200)2 + (12)2]
= 1/2 x [ 40000 + 144 ]
= 40144/2
= 20072 .
Let y x 48 = 173 x 240
Then y = (173 x 240) / 48
=173 x 5
= 865 .
The local value of 7 in 5679032 is 70000.
1014 x 986 = (1000 + 14 ) x (1000 -14)
= (1000)2 - (14)2
= (1000000 - 196) = 999804 .
Given expression = a2+b2+2ab = (a+b)2
where a = 387 and b = 114
= (387 + 114 )2
= (501)2
=(500 +1 )2
=(500)2 + (1)2+ 2 x 500 x 1
= 250000 + 1 +1000 = 251001.
Let the number be x.
Then, 11x =132
? x = 12
Let the number be x.
Then, x - 31 = 55 - x
? 2x = 55 + 31= 86
? 2x = 86
? x = 43
Let the required number is N.
Then, N/3 - N/4 = 12.
? 4N - 3N = 144
? N = 144
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