#Numbers - 19

 
While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is _________?


SOLUTION - 

                      Let the other two numbers be x and y.
                      
                      Correct Product = x*y*37
                      Incorrect Product = x*y*73

                     Difference = 720
                => 73xy - 37xy = 720
                => 36xy = 720
                => xy = 20 -----------------(i)

             Now, we know that,
           
                (x^2 + y^2)/2  ≥  (x^2 * y^2)^(1/2)    [ AM ≥ GM ]
           
           => (x^2 + y^2)  ≥ 2*(xy)
           => (x^2 + y^2) ≥ 2*20
         
          => (x^2 + y^2) ≥ 40 ANS

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