用软件解方程32x^5+3349456x^4-5941616812296x^3-585145514845851080x^2+147013447513276833423286x+15377302441624829616294559439=0有根式解,要根式解那算算这个a^2+b^2+c^2+d^2+e^2=894236993423ac+ce+bd-de-a^2/2=-999136005391ae-ac-cd-b

Question

用软件解方程
32 x^5+3349456 x^4-5941616812296 x^3-585145514845851080 x^2+147013447513276833423286 x+15377302441624829616294559439 =0
有根式解,要根式解
那算算这个
a^2+b^2+c^2+d^2+e^2=894236993423
ac+ce+bd-de-a^2/2=-999136005391
ae-ac-cd-be-b^2/2=-1033536225483/2
ae+ad+bc+bd+c^2/2=3075230855865/2
ab+bc+de+cd-e^2/2=-289030652148
的整数解

Answer 1

五次方程没有根式求根公式,一般的数学软件只能给数值解.
In[11]:= NSolve[
32 x^5 + 3349456 x^4 - 5941616812296 x^3 - 585145514845851080 x^2 +
147013447513276833423286 x + 15377302441624829616294559439 ==
0,x,10]
Out[11]= {{x -> -401258.9880},{x -> -159268.3897},{x -> \
-110135.6589},{x -> 174303.7438},{x -> 391688.7928}}
未知数和方程比较多,家用电脑恐怕会算很长时间.