If \frac{x}{b+c-a}=\frac{y}{b-c-a}=\frac{z}{a+b-c}=k, then what is x^{2}+y^{2}+z^{2}-2xy-2yz+2zx equal to?
- A. k^{2}(a^{2}+b^{2}+c^{2})
- B. k^{2}(a^{2}-b^{2}+c^{2})
- C. k^{2}(a+b+c)^{2} ✓
- D. k^{2}(a-b+c)^{2}
Correct Answer: C. k^{2}(a+b+c)^{2}
Explanation
The given expression can be written as (x-y+z)^2. Substitute the expressions: x-y+z = k(b+c-a) - k(b-c-a) + k(a+b-c) = k(a+b+c). Squaring this gives k^2(a+b+c)^2.
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