The sum of the squares of three numbers is 83, while the sum of their products…
2020
The sum of the squares of three numbers is 83, while the sum of their products taken two at a time is 71. Their sum will be
- A.
15
- B.
49
- C.
142
- D.
225
Attempted by 8 students.
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Correct answer: A
To find the sum of the three numbers, we use a standard algebraic identity.
Let the three numbers be x, y and z. We are given:
Sum of the squares: x² + y² + z² = 83
Sum of the products taken two at a time: xy + yz + zx = 71
The required identity is:
(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)
Substituting the given values:
(x + y + z)² = 83 + 2(71)
(x + y + z)² = 83 + 142 = 225
Taking the (positive) square root:
x + y + z = √225 = 15
Therefore the sum of the three numbers is 15.