CBSE Class 10 Answered
if (a+b+c)+(ab+bc+ca)+(a*b*c)=100, then find a+b+c
Asked by swetha | 27 Dec, 2013, 04:19: PM
Expert Answer
Kindly cross check, the correct statement of the given condition should be (a+b+c)+(ab+bc+ca)+(a*b*c)=1000
Answer:
Consider the product (a+1)(b+1)(c+1).
(a+1)(b+1)(c+1) = a+d+c+ab+bc+ca+abc+1
So we can rewrite the goven equation as
(a+1)(b+1)(c+1) - 1 = 1000
(a+1)(b+1)(c+1) = 1001
(a+1)(b+1)(c+1) = 7*11*13
(a+1)(b+1)(c+1) = (6+1)*(10+1)*(12+1)
Thus, a+b+c = 6+10+12=28
So we can rewrite the goven equation as
(a+1)(b+1)(c+1) - 1 = 1000
(a+1)(b+1)(c+1) = 1001
(a+1)(b+1)(c+1) = 7*11*13
(a+1)(b+1)(c+1) = (6+1)*(10+1)*(12+1)
Thus, a+b+c = 6+10+12=28
Answered by | 28 Dec, 2013, 12:47: AM
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