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The Brainliest Answer!

So, 1/x = 1/(5-2√6) , By rationalizing it we get ,

1/x =1/(5-2√6) × (5+2√6)/(5+2√6)

= (5+2√6)/(25 - 24)

= 5 +2√6

Now, x² + 1/x² = (5 - 2√6)² + (5+2√6)² = 25 - 20√6 + 24 + 25 + 20√6 + 24

= 25 + 25 +24 + 24 = 50 + 48 =

so1/x=1/5-2√6

we have to rationalise the denominator so to do it we have to multiply both the numerator and denominator with the rationalising factor of 5-2√6.The rationalising factor is 5+2√6

1/5-2√6×5+2√6/5+2√6=5+2√6

(5-2√6)²=49-20√6

(5+2√6)²=49+20√6

x²+1/x²=49-20√6 + 49+20√6

=98