Problem: The fourth power of 1+1+1\sqrt{1+\sqrt{1+\sqrt{1}}}1+1+1 is
Answer Choices:
A. 2+3\sqrt{2}+\sqrt{3}2+3
B. 12(7+35)\dfrac{1}{2}(7+3 \sqrt{5})21(7+35)
C. 1+231+2 \sqrt{3}1+23
D. 333
E. 3+223+2 \sqrt{2}3+22 Solution:
If xxx denotes the given expression, then x2=1+2x^{2}=1+\sqrt{2}x2=1+2 and x4=3+22x^{4}=3+2 \sqrt{2}x4=3+22.