التمرين 1
\( A = -\sqrt{5} + \left[ a - \frac{13}{2} - (-1.5 - b) \right] \)
\( B = (-3 + a) - \left[ \sqrt{5} + \frac{4}{5}(-5 - b) \right] \)
1- اختصر A و B
\( A = -\sqrt{5} + a - \frac{13}{2} + 1.5 + b \)
\( = a + b - \sqrt{5} - 6.5 + 1.5 \)
\( = a + b - \sqrt{5} - 5 \)
\( B = -3 + a - (\sqrt{5} - 4 - \frac{4b}{5}) \)
\( = -3 + a - \sqrt{5} + 4 + \frac{4b}{5} \)
\( = 1 + a - \sqrt{5} + \frac{4b}{5} \)
\( = a + b - \sqrt{5} - 6.5 + 1.5 \)
\( = a + b - \sqrt{5} - 5 \)
\( B = -3 + a - (\sqrt{5} - 4 - \frac{4b}{5}) \)
\( = -3 + a - \sqrt{5} + 4 + \frac{4b}{5} \)
\( = 1 + a - \sqrt{5} + \frac{4b}{5} \)
2- احسب B - A
\( B - A = (1 + a - \sqrt{5} + \frac{4b}{5}) - (a + b - \sqrt{5} - 5) \)
\( = 1 + a - \sqrt{5} + \frac{4b}{5} - a - b + \sqrt{5} + 5 \)
\( = 6 + \frac{4b}{5} - b = 6 + \frac{4b - 5b}{5} \)
\( = 6 - \frac{b}{5} \)
\( = 1 + a - \sqrt{5} + \frac{4b}{5} - a - b + \sqrt{5} + 5 \)
\( = 6 + \frac{4b}{5} - b = 6 + \frac{4b - 5b}{5} \)
\( = 6 - \frac{b}{5} \)
3- احسب B إذا كان \( a = \sqrt{3} - 2 \) و \( b = \sqrt{5} + 1 \)
\( B = 1 + (\sqrt{3} - 2) - \sqrt{5} + \frac{4(\sqrt{5} + 1)}{5} \)
\( = \sqrt{3} - 1 - \sqrt{5} + \frac{4\sqrt{5} + 4}{5} \)
\( = \frac{5(\sqrt{3} - 1 - \sqrt{5}) + 4\sqrt{5} + 4}{5} \)
\( = \frac{5\sqrt{3} - 5 - 5\sqrt{5} + 4\sqrt{5} + 4}{5} \)
\( = \frac{5\sqrt{3} - \sqrt{5} - 1}{5} \)
\( = \sqrt{3} - 1 - \sqrt{5} + \frac{4\sqrt{5} + 4}{5} \)
\( = \frac{5(\sqrt{3} - 1 - \sqrt{5}) + 4\sqrt{5} + 4}{5} \)
\( = \frac{5\sqrt{3} - 5 - 5\sqrt{5} + 4\sqrt{5} + 4}{5} \)
\( = \frac{5\sqrt{3} - \sqrt{5} - 1}{5} \)
4- أوجد b إذا كان B = -3
\( -3 = 1 + a - \sqrt{5} + \frac{4b}{5} \)
\( \Rightarrow \frac{4b}{5} = -3 - 1 - a + \sqrt{5} \)
\( \Rightarrow \frac{4b}{5} = -4 - a + \sqrt{5} \)
\( \Rightarrow b = \frac{5}{4}(-4 - a + \sqrt{5}) \)
\( \Rightarrow \frac{4b}{5} = -3 - 1 - a + \sqrt{5} \)
\( \Rightarrow \frac{4b}{5} = -4 - a + \sqrt{5} \)
\( \Rightarrow b = \frac{5}{4}(-4 - a + \sqrt{5}) \)
التمرين 2
\( A = -\sqrt{2} - (x - \sqrt{2}) - [4 - (y + \sqrt{2})] \)
1- اختصر العبارة A
\( A = -\sqrt{2} - x + \sqrt{2} - [4 - y - \sqrt{2}] \)
\( = -x - 4 + y + \sqrt{2} \)
\( = -x - 4 + y + \sqrt{2} \)
2- أوجد x - y إذا كان A = -11
\( -11 = -x + y - 4 + \sqrt{2} \)
\( \Rightarrow -x + y = -11 + 4 - \sqrt{2} \)
\( \Rightarrow -(x - y) = -7 - \sqrt{2} \)
\( \Rightarrow x - y = 7 + \sqrt{2} \)
\( \Rightarrow -x + y = -11 + 4 - \sqrt{2} \)
\( \Rightarrow -(x - y) = -7 - \sqrt{2} \)
\( \Rightarrow x - y = 7 + \sqrt{2} \)
3- احسب A في حالة: \( x = 3 \), \( y = -\sqrt{2} \)
\( A = -(3) + (-\sqrt{2}) - 4 + \sqrt{2} \)
\( = -3 - \sqrt{2} - 4 + \sqrt{2} = -7 \)
\( = -3 - \sqrt{2} - 4 + \sqrt{2} = -7 \)