Two questions, see the attached pictures.
1) I believe
e is not the right answer in this case. As you are trying to trying to find x^2 +1/x (were x = 2+/3), you should be getting 9 - 3 * sqrt{3}
and.....
Therefore....
and even if you try to somehow expand it, it is nowhere close to the correct answer.
2) Assuming your set contains 5 elements (A, B, C, D, E), you should end up with 32 subsets (inc the empty subset). The formula you should be using in thise case is:
where n is the number of elements in the set (A).
More direct way of approaching the situation is:
empty subset (containing 0 elements) - 1
{}
subsets containing 1 element - 5
{A}
{B}
{C}
{D}
{E}
subsets containing 2 elements - 10
{AB}
{AC}
{AD}
{AE}
{BC}
{BD}
{BE}
{CD}
{CE}
{DE}
subsets containing 3 elements - 10
{ABC}
{ABD}
{ABE}
{ACD}
{ACE}
{ADE}
{BCD}
{BCE}
{BDE}
{CDE}
subsets containing 4 elements - 5
{ABCD}
{ABCE}
{ABDE}
{ACDE}
{BCDE}
subsets containing 5 elements - 1
{ABCDE}
Add the amount of subsets and you will get 32, which is
d