If x=7-4 root 3 find x+(1/x)?
- 14
- 27
- 22
- 29
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.
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