if x=√5+2 , then prove that X square +1 x square =18 - Maths - Number Systems

Question

if x=√5+2 , then prove that X square +1 x square =18

Abhishek Kr. Jha · Accepted Answer

x = 5+2   
(i)⇒1x = 15+2⇒1x =  15+2×5-25-2  {rationalising the denominator}= 5-252-22= 5-25-4= 5-2⇒1x = 5-2 
(ii)Now we have;L H
S = x2+1x2 = x+1x2-2×x×1x {using the identity a2+b2 = a+b2-2ab}= x+1x2-2 = 5+2+5-22 -2      {using (i) and (ii)}= 252-2= 20-2= 18 = R
H S