Question

If x + y + z = 6, x² + y² + z² = 14, find the value of xy + yz + zx.

Answer 1

Given: x + y + z = 6, x² + y² + z² = 14

Step-wise calculation:

1. Recall the identity for the square of a sum:

(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)

2. Substitute the given values into the identity:

6² = 14 + 2(xy + yz + zx) 

36 = 14 + 2(xy + yz + zx)

3. Solve for xy + yz + zx: 

2(xy + yz + zx) = 36 – 14

2(xy + yz + zx) = 22

`xy + yz + zx = 22/2`

xy + yz + zx = 11

Therefore, the value of xy + yz + zx is 11.