Correction

Fiche 2-rev3-2

Exercice 4

Ecrire sous la forme $a+b\sqrt{c}$ les nombres suivants :

$$G = \left(5-3\sqrt{7} \right)^2 \qquad H = \left(3+4\sqrt{2} \right)^2 \qquad I=\left(2+3\sqrt{7} \right) \left(5-4\sqrt{7}\right)$$

Correction

$\begin{align} G &= \left(5-3\sqrt{7} \right)^2 \\\\
&=25 – 30\sqrt{7} +9\times 7 \\\\
&=25-30\sqrt{7} + 63 \\\\
&=88 – 30\sqrt{7}
\end{align}$

$\quad$

$\begin{align} H & = \left(3+4\sqrt{2} \right)^2 \\\\
&= 9 + 24\sqrt{2} + 16 \times 2 \\\\
&= 9 + 24\sqrt{2} + 32 \\\\
&=41+24\sqrt{2}
\end{align}$

$\quad$

$\begin{align} I&=\left(2+3\sqrt{7} \right) \left(5-4\sqrt{7}\right)\\\\
&=10-8\sqrt{7}+15\sqrt{7}-12 \times 7 \\\\
&=10+7\sqrt{7}-84\\\\
&=-74+7\sqrt{7}
\end{align}$