Let n be a positive integer. Consider the quadratic equation (n+2)x2−2(2n−1)x+(n2−4n+3)=0.
(i) Find all positive integers n for which the equation has equal real roots.
(ii) For each value of n obtained in (i), compute the common root.
(iii) Verify that the value of n obtained indeed keeps the coefficient of x2 non-zero.