شاه کلید نکات
شاه کلید سوال
معادله های زیر را به روش مربع کامل حل کنید.
الف \({x^2} + 2x = 24\)
ب \({t^2} + 3t = 3\)
پ \({n^2} - 4n + 5 = 0\)
ت \(2{r^2} + r - 2 = 0\)
الف
\(\begin{array}{*{20}{l}}{{x^2} + 2x + {{\left( {\frac{2}{2}} \right)}^2} = 24 + {{\left( {\frac{2}{2}} \right)}^2}}\\{{{\left( {x + 1} \right)}^2} = 25}\\{x + 1 = \pm 5}\\{x = 5 - 1 = 4}\\{x = - 5 - 1 = - 6}\end{array}\)
ب
\(\begin{array}{*{20}{l}}{{t^2} + 3t + {{\left( {\frac{3}{2}} \right)}^2} = 3 + {{\left( {\frac{3}{2}} \right)}^2}}\\{{{\left( {t + \frac{3}{2}} \right)}^2} = \frac{{45}}{4}}\\{t + \frac{3}{2} = \pm \frac{{3\sqrt 5 }}{2}}\\{t = - \frac{3}{2} + \frac{{3\sqrt 5 }}{2}}\\{t = - \frac{3}{2} - \frac{{3\sqrt 5 }}{2}}\end{array}\)
پ
\(\begin{array}{*{20}{l}}{{n^2} - 4n = - 5}\\{{n^2} - 4n + {{\left( {\frac{{ - 4}}{2}} \right)}^2} = - 5 + {{\left( {\frac{{ - 4}}{2}} \right)}^2}}\\{{{\left( {n - 2} \right)}^2} = - 1}\\{n - 2 = \pm \sqrt { - 1} \; \otimes }\end{array}\)
ت
\(\begin{array}{*{20}{l}}{2{\mkern 1mu} {r^2} + r = 2}\\{{r^2} + \frac{1}{2}r = 1}\\{{r^2} + \frac{1}{2}r + {{\left( {\frac{1}{4}} \right)}^2} = 1 + {{\left( {\frac{1}{4}} \right)}^2}}\\{{{\left( {r + \frac{1}{4}} \right)}^2} = \frac{{17}}{{16}}}\\{r + \frac{1}{4} = \pm \frac{{\sqrt {17} }}{4}}\\{r = - \frac{1}{4} + \frac{{\sqrt {17} }}{4}}\\{r = - \frac{1}{4} - \frac{{\sqrt {17} }}{4}}\end{array}\)
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