A student attempts to solve the following problem, where $a$ and $b$ are non-zero real numbers:
Show that if $a ^ { 2 } - 4 b ^ { 3 } \geq 0$ then there exist real numbers $x$ and $y$ such that $a = x y ( x + y )$ and $b = x y$.
Consider the following attempt:
$$\begin{aligned}
& ( x - y ) ^ { 2 } \geq 0 \\
& \text { so } \quad x ^ { 2 } + y ^ { 2 } - 2 x y \geq 0 \\
& \text { so } \quad ( x + y ) ^ { 2 } - 4 x y \geq 0 \\
& \text { so } \quad x ^ { 2 } y ^ { 2 } ( x + y ) ^ { 2 } - 4 x ^ { 3 } y ^ { 3 } \geq 0 \\
& \text { so } \quad a ^ { 2 } - 4 b ^ { 3 } \geq 0
\end{aligned}$$
Which of the following best describes this attempt?
A It is completely correct.\\
B It is incorrect, but it would be correct if written in the reverse order.\\
C It is incorrect, but the student has correctly proved the converse.\\
D It is incorrect because there is an error in line (II).\\
$\mathbf { E }$ It is incorrect because there is an error in line (III).\\
F It is incorrect because there is an error in line (IV).