Is \(\frac{x}{m}*(m^2+n^2+k^2)=xm+yn+zk\)?Multiply both part by \(m\), to get rid of fraction part and open the brackets: is \(xm^2+xn^2+xk^2=xm^2+ynm+zkm\)?

\(xm^2\) will cancel out and the question becomes: is \(xn^2+xk^2=ynm+zkm\)?

(1) \(\frac{z}{k}=\frac{x}{m}\) --> \(zm=kx\) --> substitute zm with kx --> is \(xn^2+xk^2=ynm+xk^2\) --> \(xk^2\) will cancel out and the question becomes is "\(xn^2=ynm\)?" Not sufficient.

(2) \(\frac{x}{m}=\frac{y}{n}\) --> \(xn=ym\) --> substitute ym with xn --> is \(xn^2+xk^2=xn^2+zkm\) --> \(xn^2\) will cancel out and the question becomes "is \(xk^2=zkm\)?" Not sufficient.

(1)+(2) is \(xn^2+xk^2=ynm+zkm\)? --> substitutein from (1) and (2) --> is \(xn^2+xk^2=xn^2+xk^2\)? Answer is YES. Sufficient.

Answer: C.

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