Question

解方程：(19x-x^2)/(x+1)*(x+(19-x)/(x+1))=84

Answer 1

解：(19x-x^2)/(x+1)*(x+(19-x)/(x+1))=84
[(19x-x^2)/(x+1)]*[(x^2+19)/(x+1)]=84
84(x+1)^2+(x^2+19)(x^2-19x)=0
x^4-19x^2*(x-1)+84x^2-193x+84=0
x^4-x^2*(19x-19)+(7x-12)(12x-7)=0
(x^2-7x+12)(x^2-12x+7)=0
(x-3)(x-4)(x^2-12x+7)=0
解得x1=3 x2=4
x3=[12+√(12^2-4*7)]/2=6+√29
x4=[12-√(12^2-4*7)]/2=6-√29
希望能帮到你，祝学习进步O(∩_∩)O

Answer 2

方程化简有：
X(19-X)/(X+1)*(X^2+19)/(X+1)=84
X(19-X)(X^2+19)-84*(X+1)^2=0
观察知X有一个根为3，将上面式子展开有
X^4-19X^3+19X^2-19*19X+84X^2+168X+84=0
X^4-19X^3+103X^2-193X+84=0
(X-3)(X^3-16X^2+55X-28)=0
X1=3或者X^3-16X^2+55X-28=0即(X-4)(X^2-12X+7)=0
所以X1=3，X2=4，X3=6+29^1/2，X4=6-19^1/2

Answer 3

X1=3，X2=4，X3=6+29^1/2，X4=6-19^1/2