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Aptitude Day 217

Problems on Surds and Indices:

1. Find the value of (21/4-1)(23/4+21/2+21/4+1)

Solution:
                  Let us assume 21/4 = x
  
                  Then  (21/4-1)(23/4+21/2+21/4+1) becomes  (x-1)(x3+x2+x+1)
                   (x-1)(x3+x2+x+1)= (x-1)[x2(x+1)+x+1]
                                                 =(x-1)(x+1)(x2+1)
                                                 = (x4-1)
                                                 = 21(4)/4-1 = 2-1
                                                 = 1.


2. The value of 1/(216)-2/3  +   1/(256)-3/4   +   1/(32)-1/5 is :
      
  Solution:
                 1/(216)-2/3  +   1/(256)-3/4   +   1/(32)-1/5
                 1/(63)-2/3  +   1/(44)-3/4   +   1/(25)-1/5
                 62+ 43+ 2 = 36+ 64+ 2
                                  =102.


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