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1. x(2x+y+z)=x(x+2y+z)=a,

Answer: Option C

Explanation:

\frac{x}{2 x + y + z} = a, \frac{y}{x + 2 y + z} = a, \frac{z}{x + y + 2 z} = a S o, x = 2 a x + a y + a z y = a x + 2 a y + a z z = a x + a y + 2 a z N o w, x + y + z = 2 a x + a y + a z + a x + 2 a y + a y + a x + a y + 2 a z \Rightarrow x + y + z = 4 a x + 4 a y + 4 a z \Rightarrow x + y + z = 4 a (x + y + z) \Rightarrow 4 a = 1 a = \frac{1}{4}

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