Question

(a-2)*x+2=a^2 * (3-x) +5a
Решить уравнение при всех значениях параметра a

Answer 1

(a-2)x+2=a²(3-x)+5a
(a-2)x+2=3a²-a²x+5a
(a-2)x+a²x=3a²+5a-2
(a²+a-2)x=3a²+5a-2
x=(3a²+5a-2)/(a²+a-2)

3a²+5a-2=3*(a+2)*(a-1/3)
a²+a-2=(a+2)(a-1)
x=[(a+2)*(a-1)]/[3(a+2)*(a-1/3)]
x=(a-1)/(3a-1)