question_answer

The sum of the squares of two positive numbers is 100 and difference of their squares is 28. Find the sum of the numbers

A)  12                               

B)  13

C)  14       

D)  15

Correct Answer: C

Solution :

According to question, \[{{x}^{2}}+{{y}^{2}}=100\]                                   ?(i) \[{{x}^{2}}-{{y}^{2}}=28\]                          ?(ii) According both the equations, we get             \[\therefore \]                  \[x=8\]             According the Eq. (i), we get                         \[{{y}^{2}}=100-64\]                         \[{{y}^{2}}=36\]             \[\therefore \]      \[y=6\]             So        \[x+y=8+6=14\]