найдите значение p, если корни уравнения 6х^2+3x - p = 0; если ...
найдите значение p, если корни уравнения 6х^2+3x - p = 0; если корни уравнения удовлетворяют условию x1 * x2^4 +x2 *x1^4=63/8 помогите плиз или хотя бы скажите как решать....
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17.12.2022
366
Ответ
6х^2+3x - p = 0
D = 9 +4*6*p = 9 + 24p
x = [-3 +- (9 + 24p)^0.5]/12
x1 * x2^4 +x2 *x1^4=63/8
![frac{-3+sqrt{9+24p}}{12}\ frac{-3+sqrt{9+24p}}{12}*(frac{-3-sqrt{9+24p}}{12})^{4} + frac{-3-sqrt{9+24p}}{12}*(frac{-3+sqrt{9+24p}}{12})^{4}=\ frac{-3+sqrt{9+24p}}{12}*frac{-3-sqrt{9+24p}}{12}*[(frac{-3-sqrt{9+24p}}{12})^{3} + (frac{-3+sqrt{9+24p})^{}}{12})^{3}]=\ frac{(-3)^{2}-(sqrt{9+24p})^{2}}{144}*[(frac{-3-sqrt{9+24p}}{12} + frac{-3+sqrt{9+24p}}{12})*\ *((frac{-3-sqrt{9+24p}}{12})^{2} + (frac{-3+sqrt{9+24p})}{12})^{2} - frac{-3-sqrt{9+24p}}{12}*frac{-3+sqrt{}}{12}]](https://tex.z-dn.net/?f=frac{-3+sqrt{9+24p}}{12}\ frac{-3+sqrt{9+24p}}{12}*(frac{-3-sqrt{9+24p}}{12})^{4} + frac{-3-sqrt{9+24p}}{12}*(frac{-3+sqrt{9+24p}}{12})^{4}=\ frac{-3+sqrt{9+24p}}{12}*frac{-3-sqrt{9+24p}}{12}*[(frac{-3-sqrt{9+24p}}{12})^{3} + (frac{-3+sqrt{9+24p})^{}}{12})^{3}]=\ frac{(-3)^{2}-(sqrt{9+24p})^{2}}{144}*[(frac{-3-sqrt{9+24p}}{12} + frac{-3+sqrt{9+24p}}{12})*\ *((frac{-3-sqrt{9+24p}}{12})^{2} + (frac{-3+sqrt{9+24p})}{12})^{2} - frac{-3-sqrt{9+24p}}{12}*frac{-3+sqrt{}}{12}] "frac{-3+sqrt{9+24p}}{12}\ frac{-3+sqrt{9+24p}}{12}*(frac{-3-sqrt{9+24p}}{12})^{4} + frac{-3-sqrt{9+24p}}{12}*(frac{-3+sqrt{9+24p}}{12})^{4}=\ frac{-3+sqrt{9+24p}}{12}*frac{-3-sqrt{9+24p}}{12}*[(frac{-3-sqrt{9+24p}}{12})^{3} + (frac{-3+sqrt{9+24p})^{}}{12})^{3}]=\ frac{(-3)^{2}-(sqrt{9+24p})^{2}}{144}*[(frac{-3-sqrt{9+24p}}{12} + frac{-3+sqrt{9+24p}}{12})*\ *((frac{-3-sqrt{9+24p}}{12})^{2} + (frac{-3+sqrt{9+24p})}{12})^{2} - frac{-3-sqrt{9+24p}}{12}*frac{-3+sqrt{}}{12}]")
![frac{9-9-24p}{144}*[(frac{-6}{12})*(frac{9+9+24p+9+9+24p}{144} - frac{9-9-24p}{144})]=\ =-frac{p}{6}*[(-frac{1}{2})*(frac{36+48p}{144} + frac{24p}{144})]=\ =frac{p}{12}*frac{36p+72p}{144} = frac{63}{8}\ 36p+72p^{2} = 12*63*18\ 36p+72p^{2} = 13608\ p+2p^{2} = 378\ 2p^{2} +p - 378 = 0\ D = 1 + 4*2*378 = 3025 = 55^{2}\ p = frac{-1 ^{+}_{-} 55}{4}\ p_{1} = 13,5\ p_{2} = -14](https://tex.z-dn.net/?f=frac{9-9-24p}{144}*[(frac{-6}{12})*(frac{9+9+24p+9+9+24p}{144} - frac{9-9-24p}{144})]=\ =-frac{p}{6}*[(-frac{1}{2})*(frac{36+48p}{144} + frac{24p}{144})]=\ =frac{p}{12}*frac{36p+72p}{144} = frac{63}{8}\ 36p+72p^{2} = 12*63*18\ 36p+72p^{2} = 13608\ p+2p^{2} = 378\ 2p^{2} +p - 378 = 0\ D = 1 + 4*2*378 = 3025 = 55^{2}\ p = frac{-1 ^{+}_{-} 55}{4}\ p_{1} = 13,5\ p_{2} = -14 "frac{9-9-24p}{144}*[(frac{-6}{12})*(frac{9+9+24p+9+9+24p}{144} - frac{9-9-24p}{144})]=\ =-frac{p}{6}*[(-frac{1}{2})*(frac{36+48p}{144} + frac{24p}{144})]=\ =frac{p}{12}*frac{36p+72p}{144} = frac{63}{8}\ 36p+72p^{2} = 12*63*18\ 36p+72p^{2} = 13608\ p+2p^{2} = 378\ 2p^{2} +p - 378 = 0\ D = 1 + 4*2*378 = 3025 = 55^{2}\ p = frac{-1 ^{+}_{-} 55}{4}\ p_{1} = 13,5\ p_{2} = -14")
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17.12.2022
