If the given equation is true for all values of   where   is a constant, then what is the value of  ?

To find the value of , we need to analyze the given equation. Since the equation is true for all values of , it means that the equation holds for any value we substitute for .

Let's assume that the equation is:

Equation:

To determine the value of , we can use any value for and solve for . Since the equation holds for all values of , we can choose any value to substitute.

Let's substitute a value of into the equation:

Equation:

Simplifying the equation:

Equation:

Since the equation is true for all values of , the left side of the equation should be equal to the right side for any value of we choose. Therefore, we can equate the coefficients of the terms on both sides of the equation.

Comparing the coefficients:

Coefficient of on the left side: Coefficient of on the right side:

Since the coefficients of the terms on both sides of the equation are equal, we can set them equal to each other:

Simplifying the equation:

Now, we can solve for :

Therefore, the value of is .