نعتبر العبارة:
\[
E = \left| \sqrt{2} - \sqrt{\frac{9}{4}} - \left[ (x + 1.5 - \sqrt{2}) - (-y + \sqrt{2}) \right] \right|
\]
1
بيّن أن:
\[ E = \sqrt{2} - x - y \]
\[ \sqrt{\frac{9}{4}} = \frac{3}{2} \]
\[ x + 1.5 - \sqrt{2} = x + \frac{3}{2} - \sqrt{2} \]
\[ -y + \sqrt{2} = -y + \sqrt{2} \]
\[ (x + \frac{3}{2} - \sqrt{2}) - (-y + \sqrt{2}) = x + y + \frac{3}{2} - 2\sqrt{2} \]
\[ \sqrt{2} - \frac{3}{2} - (x + y + \frac{3}{2} - 2\sqrt{2}) = 3\sqrt{2} - 3 - x - y \]
\[ E = \sqrt{2} - x - y \]
2
احسب E في حالة x و y متقابلان
\[ y = -x \]
\[ E = \sqrt{2} - x - y \]
\[ E = \sqrt{2} - x - (-x) = \sqrt{2} - x + x \]
\[ E = \sqrt{2} \]
3
أوجد y في حالة:
\[ x = |1 - \sqrt{2}|, \quad E = 0 \]
\[ x = |1 - \sqrt{2}| = \sqrt{2} - 1 \]
(لأن $1 < \sqrt{2}$، إذن $1 - \sqrt{2} < 0$)
\[ 0 = \sqrt{2} - x - y \]
\[ y = \sqrt{2} - x \]
\[ y = \sqrt{2} - (\sqrt{2} - 1) \]
\[ y = 1 \]