The sum of squares of 3 numbers is 170, while the sum of their products taken…
2024
The sum of squares of 3 numbers is 170, while the sum of their products taken two at a time is 157.
What is the sum of the numbers?
- A.
20
- B.
22
- C.
24
- D.
28
Attempted by 22 students.
Show answer & explanation
Correct answer: B
Key identity: (a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab+bc+ca).
Given a^2 + b^2 + c^2 = 170 and ab + bc + ca = 157.
Compute (a+b+c)^2:
(a+b+c)^2 = 170 + 2·157 = 170 + 314 = 484.
Therefore a+b+c = ±√484 = ±22.
Because the numerical choices include 22, the sum of the numbers (as presented among the answer choices) is 22.