Saved Bookmarks
| 1. |
If A,B,C are positive integers such that A+B+C+AB+BC+AC+ABC=100then A+B+C???? |
|
Answer» bc+ca+a+B+c=1000then what is the value of a+b+cThe solution to this problem BEGINS by ADDING 1 to both sides of the equation.So,abc+ab+bc+ca+a+b+c+1=1000+1This can be reduced to,ab.(c+1)+b.(c+1)+a.(c+1)+(c+1)=1001This can be further reduced to,(c+1).(ab+b+a+1)=1001Which REDUCES to,(a+1).(b+1).(c+1)=7×11×13Since exact values of a,b,care not required, so ORDER of factors is not important, so in any order,a=7−1=6b=11−1=10a=13−1=12∴a+b+c=6+10+12=28 |
|