question_answer 8)

Verify \[a-\left( -b \right)=a+b\] for the following values of a and b. (i) \[~a=21,\,b=18\]        (ii) \[a=118,\,\,b=125\]  (iii)\[~a=75,\,\,b=84\]    (iv) \[a=28,\text{ }b=11\]

Answer:

                (i) \[~a=21,\,b=18\] L.H.S.\[=a-\left( -\text{ }b \right)=21-\left( -18 \right)=21+18=39\]                         ... (1) R.H.S. \[=a+b=21+18=39\]                                                           ... (2) From (I) and (2), we get \[a-\left( -\text{ }b \right)=a\text{ }+\text{ }b\] (ii) \[a=118,b=125\] L.H.S. \[=a-\left( -\text{ }b \right)=118-\left( -\text{ }125 \right)\] \[=118+125=243\]                                                         ... (1) R.H.S. \[=a+b=118+125=243\]                                                   ... (2) From (1) and (2), we get \[a-\left( -b \right)=a+b\]  (iv) \[a=75,b=84\] L.H.S.\[=a-\left( -\text{ }b \right)=75-\left( -\text{ }84 \right)=75+84=159~\]                   ... (1) R.H.S. \[~=a+b=75+84=159~~\]                                                 ? (2) From (1) and (2), we get \[a-(-b)=a+b\] (iv) \[a=28,b=11\] L.H.S.\[=a-\left( -\text{ }b \right)=28-\left( -\text{ }11 \right)=28\text{ }+11=39\]                              ... (1) R.H.S.\[=a+b=28+11=39\]                                                            ... (2) From (i) and (2), we get \[a-(-b)=a+b\]