Answers

2014-08-21T12:52:59+05:30
Let us consider A and B as the number ; given , AB = 120 ; A2 + B2 = 289. Let us rearrange to simplify in formula : A2+B2 = (A + B)2 = A2 + B2 + 2AB we know the value for AB and A2+B2 sub in the equ;(A2+B2) = 289+ (2 x 120) = 529 A+ B =sqrt 529 = 23 is the sum of the value.
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120=120*1 or 60*2 or 30*4 or 20*6 or15*8
sorry missing data here ......or 10*12 now in 1st, 2nd and 3rd case the square of two number is more than 289, then these combination are not possible.., 15^2+8^2=289,hence answer is 15+8=23
2014-08-21T13:05:14+05:30
Let the numbers be x and y.
Then,xy = 120 and x² + y² = 289 
⇒ (x + y)² = x² + y² + 2xy
               = 289 + 2 * 120
               = 289 + 240
               = 529
⇒ x + y  = √529
         = 23
The sum of the two number is 23.
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The 2 numbers are 15 and 8.
15 + 8 = 23 and 15square + 8square = 289.