If $$x^2 + 5y^2 + z^2 = 2y(2x+z)$$, then which of the following statements is(are) necessarily true?
A. x = 2y B. x = 2z C. 2x = z
The equation is not satisfied for only x = 2y.
Using statements B and C, i.e., x = 2z and 2x = z, we see that the equation is not satisfied.
Using statements A and B, i.e., x = 2y and x = 2z, i.e., z = y = x/2, the equation is satisfied.
Option c) is the correct answer.
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