Question

find two consecutive even natural numbers whose product is 168

Answer 1

let the two consecutive natural no. be :  x and x+2
 
                  so , x * x+2 = 168 
                    
                              => x^2 + 2x = 168
                              => x^2 +2x - 168 = 0 
                              => x^2 - 14x -12x - 168  (by splitting the middle term)
                              => x(x+14) -12 (x+14) 
 from the above we get , => (x-12) = 0 ; (x+14) = 0 
                       therefore => x=12 , x= -14
                                                                    
                       since, negative term is negligible  
            so x=12 is accepted 
          
          IF, x = 12 and x+ 2 = 12+2= 14


so, two consecutive even natural numbers whose product is 168 =14,12

      NOTE : x^2 is x square
             and (*) is multiplication symbol
  
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Answer 2

let natural no. be x and x+2
x(x+2)=168
x^2+2x-168=0
x^2+14x-12x-168=0
x(x+14)-12(x+14)
(x-12)(x+14)
x=12
x= -14
minus is negligible
so, x=12
x+2=12+2=14