Olympiad workbookIOQMBasics of Mathematics
If a, b, c 4 are integers, not all equal, and 4 a b c=(a+3)(b+3)(c+3) , then what is the value of a+b+c ?
Correct answer
16
Step-by-step solution
aligned & 4 a b c=27+3(a b+b c+c a)+9(a+b+c)+a b c & 3 a b c=27+3(a b+b c+c a)+9(a+b+c) & a b c=9+(a b+b c+c a)+3(a+b+c) & a b c-(a b+b c+c a)+(a+b+c)-1=8+4(a+b+c) & (a-1)(b-1)(c-1)=8+4(a+b+c) aligned Put a -1= A , b -1= B , c -1= C , array ll & A B C=20+4(A+B+C) & A= 4(5+B+C) B C-4 & B=3, C=4, A=6 array or they can be interchanged array ll & (a, b, c) are anangemets of (4,5,7) & a+b+c=16 array