Consider the following statements in respect of the expression

S_ⁿ=n(n+1)2

where n is an integer :

1. There are exactly two values of n for which S_n = 861.
2. S_n = S_-(n+1) and hence for any integer m, we have two values of n for which S_n=m.

Which of the above statements is/are correct

If the sum of the roots of ax²+bx+c = 0 is equal to the sum of the squares of their reciprocals, then which one of the following relations is correct

If a³ = 117+b³ and a= 3+b, then the value of a+b is (given that a>0 and b>0)

If 

x= √a+2b+√aa-2b/√a+2b-√a-2b

then bx²-ax+b is equal to (given that b ≠ 0)

If the linear factors of ax² - (a²+1) x+a are p and q, then p+q is equal to 

If 4^x2^y = 128 and 3^3x3^2y-9^xy = 0, then the value of x+y can be equal to