Question

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....

Answer 1

 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

$frac{-3+sqrt{9+24p}}{12}\ frac{-3+sqrt{9+24p}}{12}*(frac{-3-sqrt{9+24p}}{12})^{4} + frac{-3-sqrt{9+24p}}{12}*(frac{-3+sqrt{9+24p}}{12})^{4}=\ frac{-3+sqrt{9+24p}}{12}*frac{-3-sqrt{9+24p}}{12}*[(frac{-3-sqrt{9+24p}}{12})^{3} + (frac{-3+sqrt{9+24p})^{}}{12})^{3}]=\ frac{(-3)^{2}-(sqrt{9+24p})^{2}}{144}*[(frac{-3-sqrt{9+24p}}{12} + frac{-3+sqrt{9+24p}}{12})*\ *((frac{-3-sqrt{9+24p}}{12})^{2} + (frac{-3+sqrt{9+24p})}{12})^{2} - frac{-3-sqrt{9+24p}}{12}*frac{-3+sqrt{}}{12}]$

 

$frac{9-9-24p}{144}*[(frac{-6}{12})*(frac{9+9+24p+9+9+24p}{144} - frac{9-9-24p}{144})]=\ =-frac{p}{6}*[(-frac{1}{2})*(frac{36+48p}{144} + frac{24p}{144})]=\ =frac{p}{12}*frac{36p+72p}{144} = frac{63}{8}\ 36p+72p^{2} = 12*63*18\ 36p+72p^{2} = 13608\ p+2p^{2} = 378\ 2p^{2} +p - 378 = 0\ D = 1 + 4*2*378 = 3025 = 55^{2}\ p = frac{-1 ^{+}_{-} 55}{4}\ p_{1} = 13,5\ p_{2} = -14$