Question

if x=2+√3, find the value of x square+1/x square.

Answer 1

Hey ,
The answer is 14.

Here the solution.


x²+1/x² = (2+√3)²+1/(2+√3)² = (4+3+4√3)+1/(4+3+4√3) = (7+4√3)+1/(7+4√3) = (7+4√3)²+1/(7+4√3) = (49+48+56√3+1)/(7+4√3) = [(98+56√3)/(7+4√3)]×[(7-4√3)/(7-4√3)] = [(98+56√3)(7-4√3)]/7²-(4√3)² = (686+392√3-392√3-672)/(49-48) = 14/1 = 14

Hope it's helpful to uh.
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Thankyou.