If x + y + z = 10 and $$\text x^2+\text y^2+\text z^2=80$$​, then what is the value of 4xy + 4yz + 4zx?

Correct option is C

Given:

• x + y + z = 10
• x² + y² + z² = 80
• We need to find the value of 4xy + 4yz + 4zx

Formula Used:

We use the identity:

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

Solution:

Step 1:
(x + y + z)² = 10² = 100

Step 2:
Substitute values in the identity:

100 = 80 + 2(xy + yz + zx)

Step 3:
100 – 80 = 2(xy + yz + zx)
20 = 2(xy + yz + zx)
So, xy + yz + zx = 10

Step 4:
Now multiply by 4:

4xy + 4yz + 4zx = 4 × 10 = 40

Final Answer: (C) 40