Sum of products of three numbers taken two at a time is 131.
Sum of products of three numbers taken two at a time is 131. Sum of squares of the three numbers is 138. What is the sum of the three numbers?
Answer/Solution
20
Steps/Work
Explanation:
All the data given in the question points to the equation mentioned below:
Considering the three numbers to be a,b and c:
(a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Accordingly, substitute for a, b and c and solve:
=> a2+b2+c2= 138, ab+bc+ac = 131. Thus, 2(ab+bc+ac)= 2*131= 262
(a+b+c)2= 138+262= 400.
Therefore, a+b+c= 20
ANSWER: A
All the data given in the question points to the equation mentioned below:
Considering the three numbers to be a,b and c:
(a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Accordingly, substitute for a, b and c and solve:
=> a2+b2+c2= 138, ab+bc+ac = 131. Thus, 2(ab+bc+ac)= 2*131= 262
(a+b+c)2= 138+262= 400.
Therefore, a+b+c= 20
ANSWER: A