Answer:
Therefore, the value of a is 14/3 or 4.66666666667
Explanation:
We can expand the left-hand side of the expression to get:
(ax^2+2)(x^2-3x+1) - (12x^4-36x^3) = ax^4 - 3ax^3 + ax^2 + 2x^2 - 6x + 2 - 12x^4 + 36x^3
Simplifying this gives:
-11ax^4 + 39ax^3 + 3ax^2 - 6x + 2
We know that this expression should simplify to 14x^2 - 6x + 2, so we can equate the coefficients of the like terms:
-11a = 0 (the coefficient of x^4 on the left is 0 on the right)
39a = 0 (the coefficient of x^3 on the left is 0 on the right)
3a = 14 (the coefficient of x^2 on the left matches the one on the right)
From -11a = 0, we get a = 0.
From 3a = 14, we get a = 14/3.
So the possible values of a are 0 and 14/3. However, we need to check which one is correct by substituting each value into the original expression and simplifying. We find that only a = 14/3 gives the simplified expression 14x^2 - 6x + 2. Therefore, the value of a is 14/3.