Let the required number is N.
Then, N/3 - N/4 = 12.
? 4N - 3N = 144
? N = 144
Let the number be x.
Then, x - 31 = 55 - x
? 2x = 55 + 31= 86
? 2x = 86
? x = 43
Let the number be x.
Then, 11x =132
? x = 12
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.
1014 x 986 = (1000 + 14 ) x (1000 -14)
= (1000)2 - (14)2
= (1000000 - 196) = 999804 .
1299 x 1299 = (1299)2
= (1300 - 1)2
= (1300)2 + (1)2 - 2 x 1300 x 1
= 1690000 + 1 - 2600 = 1687401
Let the original number be N.
So from question N - 3N/4 = 19
? 4N - 3N = 76
? N = 76
Let the number be N.
Then, N/5 - 5 = 5
? N - 25 = 25
? N = 50
Let the number be N.
So from question 2N/5 + 25 = N
? 2N + 125 = 5N
? 3N = 125
? N = 125/3
Let the required number be N.
So 3/4 x 1/5 x N = 60
? 3N / 20 = 60
? N = 400
Let the two number be x and (x + 1)
Then, (x+1)2 - x2 = 35
? 2x = 34
? x = 17
So, the number are 17 and 18
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