A. The solutions to the equation x^2 = 9 are x = 3 and x = -3.
B. There is more than one solution to the equation x^2 = 9 because when we square a number, both the positive and negative values of that number will yield the same result. In this case, 3^2 and (-3)^2 both equal 9.
C. The equation xn = c will have two solutions when the value of n is even. This is because even exponents preserve the sign of the base, so both positive and negative values of the base will yield the same result when raised to an even power.
D. If c is a negative number in the equation xn = c, it does not affect our ability to solve the equation for different values of n. The solutions will still exist and depend on the value of n. However, the solutions will be negative since the base raised to any positive power will result in a positive value, while the negative value of c will require a negative base.
E. The relationship between c1 and c2 that allows us to find solutions for the equation xn + c1 = c2, regardless of the value of n, is c1 = c2. When c1 and c2 are equal, we can subtract c1 from both sides of the equation, resulting in xn = 0. The solution to xn = 0 is x = 0 for any value of n.
~~~Harsha~~~