Partons du fait que $5 < 7$:
\begin{align*}
5 < 7 & \iff \sqrt5 < \sqrt7\\
      & \iff -\sqrt5 > -\sqrt7\\
      & \iff 2-\sqrt5 > 2-\sqrt7.
\end{align*}
De plus,
\begin{align*}
4 < 5 & \iff \sqrt4 < \sqrt5\\
      & \iff 2 < \sqrt5\\
      & \iff 2-\sqrt5 < 0.
\end{align*}
On a donc:
\[
2-\sqrt7 < 2-\sqrt5 < 0.
\]
On en conclut alors que:
\[
0 < \big(2-\sqrt5\big)^2 < \big(2-\sqrt7\big)^2.
\]
