154402

For part c)
1 Square both sides
2 23-6sqrt(6-4sqrt(2))=a+2sqrt(ab)+b
3 a+b=23
4 2sqrt(ab)=-6sqrt(6-4sqrt(2))
5 sqrt(ab)=-3sqrt(6-4sqrt(2))
6 ab=54-36sqrt(2)
7 a=23-b
8 Plugging 23-b for a into line 6, we get
9 b(23-b)=54-36sqrt(2)
10 b(b-23)=36sqrt(2)-54
11(b^2)-23b+54-36sqrt(2)=0
12 b=1/2(23-sqrt(313+144sqrt(2))) and
13 a=1/2(23+sqrt(313+144sqrt(2)))
14 or vice versa