ExplanationPlugging in 2 for y gives you \(x^2 = 5\) in the given equation and 17 for Quantity B.

Squaring this gives you \(x^4 = 25\) for Quantity A, which is therefore larger.

Plugging in any other number gives the same result.

Alternatively, doing algebra by squaring both sides of the given equation reveals Quantity A: \(x4 = (y^2 + 1)(y^2 + 1) = y^4 + 2y^2 + 1\).

The only difference between Quantities A and B is the \(2y^2\) in Quantity A.

You are told that y ≠ 0, so \(2y^2\) is always positive, and Quantity A will always therefore be larger. The answer is choice (A).

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Sandy

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