Hello could someone help explain how to do these questions with working? 8 (ii) for the first and 8 (a) (iii) (iv) for the second.

Question 8 ? (a) The numbers p, q and s are fixed and positive. Also p > 1, q > 1 and P= q q- 1 i. What positive value of t minimises the expression 2 f (t) = + p - - st? ii. Show that for all t > 0, SP p 2 st iii. Prove by induction that 4 (172 X . . . X In) S n\fQuestion 8. (a) Consider the degree n version of the AM/GM inequality which states for positive real numbers x 1, X2, ..., *n that Xitx2 + " + Xn n 2 1 X1X2 ." Xn (i) Prove that if the AM/GM inequality is true for n = k, then it will be true for n = 2k (ii) Prove that if the AM/GM inequality is true for n = k, then it will be true for n = k - 1