Intrinsic and time value of an OTM put

A stock trades at $17$. A European put on it with strike $15$ is worth $7.2$. With $I$ the put's intrinsic value and $E$ its extrinsic (time) value, compute $I^2+E^2$.

$51.84$. Exercising now would pay $\max(15-17,0)=0$, so $I=0$ and the whole price is extrinsic, $E=7.2$, giving $7.2^2=51.84$.