\(\displaystyle{ x^2 - \frac{7616}{1232}x - \frac{226576}{1232}=0}\)
\(\displaystyle{ x^2 - 2 \frac{3808}{1232}x + \left(\frac{3808}{1232}\right)^2 - \left(\frac{3808}{1232}\right)^2 + \frac{226576}{1232} =0}\)
\(\displaystyle{ \left( x- \frac{3808}{1232} \right)^2 - \frac{3808^2 +226576\cdot 1232}{(1232)^2} = \left( x- \frac{3808}{1232} \right)^2 - \left( \frac{17136}{1232}\right)^2 = \left( x - \frac{3808}{1232}-\frac{17136}{1232}\right)\cdot \left( x - \frac{3808}{1232}+\frac{17136}{1232}\right)= \left( x -\frac{20944}{1232}\right) \left(x + \frac{13328}{1232}\right)= \left(x - 17\right) \left( x +\frac{119}{11}\right) = 0.}\)
\(\displaystyle{ x_{1} = 17, \ \ x_{2}= - \frac{119}{11}.}\)-- 27 wrz 2017, o 10:46 -- Drugi sposób (ogólny)
\(\displaystyle{ x^2 - \frac{b}{d}x - \frac{c}{d} =0}\)
\(\displaystyle{ x^2 -2\frac{b}{2d}x - \frac{c}{d}=0}\)
\(\displaystyle{ x^2 - 2\frac{b}{2d}+\left(\frac{b}{2d}\right)^2 -\left(\frac{b}{2d}\right)^2 -\frac{c}{d} =0}\)
\(\displaystyle{ \left ( x -\frac{b}{2d}\right)^2 - \frac{b^2 +4cd}{4d^2} =0}\)
\(\displaystyle{ \left(x -\frac{b}{2d}\right)^2 - \left(\frac{\sqrt{b^2 +4cd}}{2d}\right)^2 =0}\)
\(\displaystyle{ \left( x - \frac{b}{2d} - \frac{\sqrt{b^2 +4cd}}{2d}}\right)\left( x - \frac{b}{2d} +\frac{\sqrt{b^2 +4cd}}{2d}}\right)= 0}\)
\(\displaystyle{ \left( x - \frac{b +\sqrt{b^2 +4cd}}{2d}\right)\left( x - \frac{b -\sqrt{b^2 +4cd}}{2d}\right)=0}\)
\(\displaystyle{ x_{1}= \frac{b +\sqrt{b^2 +4cd}}{2d}, \ \ x_{2}= \frac{b -\sqrt{b^2 +4cd}}{2d}.}\)
Podstawiając: \(\displaystyle{ b = 7616, \ \ c = 226576, \ \ d = 1232}\)
otrzymujemy
\(\displaystyle{ x_{1} = \frac{7616 + \sqrt{(7616)^2 + 4\cdot 226576\cdot 1232}}{2\cdot 1232}= 17}\)
\(\displaystyle{ x_{2} = \frac{7616 - \sqrt{(7616)^2 + 4\cdot 226576\cdot 1232}}{2\cdot 1232}= -\frac{119}{11}.}\)
Obliczanie niewiadomej
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Dilectus
- Użytkownik
- Posty: 2649
- Rejestracja: 1 gru 2012, o 00:07
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Re: Obliczanie niewiadomej
Lepiej by było najpierw skrócić te ułamki
\(\displaystyle{ \frac{7616}{1232}= \frac{2^6\cdot 7 \cdot 17}{2^4 \cdot 7 \cdot 11}= \frac{4 \cdot 17}{11}}\)
\(\displaystyle{ \frac{226576}{1232}= \frac{2^4 \cdot 7^2 \cdot 17^2}{2^4 \cdot 7 \cdot 11}= \frac{7 \cdot 17^2}{11}}\)
\(\displaystyle{ \frac{7616}{1232}= \frac{2^6\cdot 7 \cdot 17}{2^4 \cdot 7 \cdot 11}= \frac{4 \cdot 17}{11}}\)
\(\displaystyle{ \frac{226576}{1232}= \frac{2^4 \cdot 7^2 \cdot 17^2}{2^4 \cdot 7 \cdot 11}= \frac{7 \cdot 17^2}{11}}\)
Ostatnio zmieniony 27 wrz 2017, o 14:22 przez Dilectus, łącznie zmieniany 1 raz.
