گام به گام کاردرکلاس صفحه 19 درس 1 حسابان یازدهم (جبر و معادله)

\(\begin{array}{*{20}{l}}\begin{array}{l}\frac{1}{{{{\left( {x - 2} \right)}^2}}} + \frac{2}{{x - 2}} = 3\mathop \Rightarrow \limits^{ \times {{\left( {x - 2} \right)}^2}} \\\\1 + 2\left( {x - 2} \right) = 3{\left( {x - 2} \right)^2}\\\\ \Rightarrow 2x - 3 = 3{x^2} - 12x + 12\end{array}\\\begin{array}{l}\\ \Rightarrow 3{x^2} - 14x + 15 = 0\\\\ \Rightarrow \Delta = {\left( {14} \right)^2} - 4\left( 3 \right)\left( {15} \right) = 16\\\\ \Rightarrow x = \frac{{14 \pm 4}}{6} \Rightarrow \left\{ {\begin{array}{*{20}{l}}{{x_1} = 3}\\{{x_2} = \frac{5}{3}}\end{array}} \right.\end{array}\end{array}\)

\(\begin{array}{l}\frac{L}{w} = \frac{{w + L}}{L} \Rightarrow {L^2} = {w^2} + wL\;\;\:\left( i \right)\\\\2\left( {w + L} \right) = 144 \Rightarrow w + L = 72 \Rightarrow w = 72 - L\;\;\:\left( {ii} \right)\\\\\mathop \Rightarrow \limits^{\left( i \right),\left( {ii} \right)} {L^2} = {\left( {72 - L} \right)^2} + \left( {72 - L} \right)L\\\\ \Rightarrow {L^2} = 5184 - 144L + {L^2} + 72L - {L^2}\\\\ \Rightarrow {L^2} = 5184 - 72L \Rightarrow {L^2} + 72L - 5184 = 0\\\\ \Rightarrow \Delta = {\left( {72} \right)^2} - 4\left( 1 \right)\left( { - 5184} \right)\\\\ \Rightarrow \Delta = 25920 = 5 \times 5184 = 5{\left( {72} \right)^2}\\\\ \Rightarrow L = \frac{{ - 72 \pm 72\sqrt 5 }}{2}\\\\ \Rightarrow \left\{ {\begin{array}{*{20}{l}}{L = \frac{{ - 72 - 72\sqrt 5 }}{2}\;\; \otimes }\\{L = \frac{{ - 72 + 72\sqrt 5 }}{2} = \frac{{\sqrt 5 - 1}}{2} \times 72}\end{array}} \right.\\\\ \Rightarrow w = 72 - L = 72 - \frac{{\sqrt 5 - 1}}{2} \times 72 = \frac{{3 - \sqrt 5 }}{2} \times 72\end{array}\)