Question

If x=5-2√6, find: x^2+1/x^2. Please show along with steps.

Answer 1

x = 5-2√6 (given)
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 = 98

Answer 2

given x=5-2√6

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