Final answer:
The value of x²/yz + y²/zx + z²/xy when x + y + z = 0 is -1.
o, the value of the expression is 3
The correct answer is:A. 3
Step-by-step explanation:
To find the value of x²/yz + y²/zx + z²/xy when x + y + z = 0, we can substitute the value of z from the given equation into the expression:
(x²/yz) + (y²/zx) + (z²/xy) = (x²/xy) + (y²/x(-x-y)) + ((-x-y)²/xy)
Simplifying further, we get:
(x²/xy) + (y²/x(-x-y)) + ((-x-y)²/xy) = (x/(-x-y)) + (y/x) + ((-x-y)/(-x-y))
Since x + y + z = 0, we can substitute -x-y for z and simplify the expression:
(x/(-x-y)) + (y/x) + ((-x-y)/(-x-y)) = (x/(-x-y)) + (y/x) - 1
Therefore, the value of x²/yz + y²/zx + z²/xy is actually equal to -1.