Question

49 Solve without calculation:
(0.07*0.07*0.07-0.05*0.05*0.05) / (0.07*0.07+0.07*0.05+0.05*0.05) = ?

Answer 1

See,
       Numerator = 0.07*0.07*0.07-0.05*0.05*0.05
                         =0.07³-0.05³
                   Since, a³-b³=(a-b)(a²+ab+b²)
                    Therefore,
             0.07³-0.05³=(0.07-0.05)(0.07²+0.07*0.05+0.05²)
                                [ Taking 0.07 in place of a and 0.05 in place of b ]
       Denominator=0.07*0.07+0.07*0.05+0.05*0.05
                           =0.07²+0.07*0.05+0.05²
       Therefore,
       Fraction=(0.07-0.05)(0.07²+0.07*0.05+0.05²)/(0.07²+0.07*0.05+0.05²)
             =(0.07-0.05)*1/1
     Value =(0.07-0.05)*1/1
               =0.07-0.05
               =0.02
            (Solved)