= Solution
Assume perfect cloning of both specified <pure states>. Allowing irrelevant output <global phases>, this would require
$$
U|00\rangle=e^{i\alpha}|00\rangle,
\qquad U|+0\rangle=e^{i\beta}|++\rangle.
$$
A <unitary operator> preserves <inner products>, and therefore their magnitudes. But the input overlap and required output overlap have different magnitudes:
$$
\boxed{|\langle00|+0\rangle|=\frac1{\sqrt2}
\ne\frac12=|\langle00|++\rangle|.}
$$
This contradiction proves that \b[no such two-qubit unitary exists], without assuming the <no-cloning theorem>.
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