Question

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. \( 2x = z \)

• A. Only A
• B. B and C
• C. A and B
• D. None of these

Hint:

When testing algebraic relationships, substitute values for the variables to identify possible conditions that hold true.

Answer 1

The Correct Option is D

The given equation is: \[ x^2 + 5y^2 + z^2 = 2y(2x + z). \] By simplifying and testing various values of \( x \), \( y \), and \( z \), none of the statements \( A \), \( B \), or \( C \) hold true for all cases. Thus, the Correct Answer is none of these.