Explanation

x = 7 — 4√3, we are required to find x + 1/x.

1/x = 1/(7 — 4√3)

Rationalising 1/x,

1/x = {1/(7 —4√3)} × {(7 + 4√3)/7 + 4√3)} = {(7 + 4√3)}/{7² — 4²(√3)²} = (7 + 4√3)/(49 — 48) = 7 + 4√3.

Therefore

x + 1/x = 7 — 4√3 + 7 + 4√3 = 14.