Answer:
The solution set is {1, -2/3, 2/3}.
Step-by-step explanation:
81m^3-81m^2-36m+36=0
9(9m^3 - 9m^2 - 4m + 4) = 0
Looks like 1 might be one root:
f(1) = = 9*1 - 9*1 - 4*1 + 4 = 0 so one factor is (x - 1).
Divide the function by x - 1:
9m^2 - 4 <------------------Quotient
----------------------------------
m - 1 ) 9m^3 - 9m^2 - 4m + 4
9m^3-9m^2
-----------------------
-4m + 4
-4m + 2
..............
Now :
9m^2 - 4 = (3m - 2)(3m + 2).
so m - 1 = 0 or 3m - 2 = 0 or 3m + 2 = 0
m = 1 , 2/3, -2/3.
