Question

if x = 5 - 2 √6, then find x² + 1/x²​

Answer 1

Answer:

If x = 5 + 2√6

Then x² = (5+2√6)² = 5² + 2(5)(2√6) + (2√6)² = 49 + 20√6

Then 1\x² =      1        

              ( 49 + 20√6)

Now, rationalising the denominator, we get,

1               ×        49 - 20√6

49 + 20√6             49 - 20√6

 

=  49 - 20√6

Now, solve the equation

x² + 1/x² =  [ 49 + 20√6 ] + [ 49 - 20√6 ]

            =  49 + 20√6 + 49 - 20√6

            =  98 Is the answer