Friday, May 17, 2024

 3.If ab = xy , then (a +b) ≠ (x+y) ,which smaller ? what will be its difference ?

     If the two numbers in the pair are widely separated, its sum will be larger  .  e.g., 8x 3 = 6x4 = 24

8 and 3 are widely separated than 6 and 4, hence the sum  8 + 3 =11 is larger than the sum 6 + 4 = 10.

Let ab = xy

(a+b)2  =  a2 + b2 + 2ab  or  2ab = (a+b)2  -  a2 - b2  and

(x+y)2  =  x2 + y2 + 2xy  or  2xy = (x+y)2  - x2 - y2

Invariably It satisfies the relation (a+b)2  -  a2 - b2   = (x+y)2  - x2 - y2 or (a+b)2 -  (x+y)2 = a2 + b2 - x2 - y2

If  ab = xy ,then  (a+b)2  + (x-y)2 =  (a-b)2  + (x+y)2

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