Question

find x^2+1/x^2 if x=2+√5​

Answer 1

Answer:

18

Step-by-step explanation:

x=2+√5

Then,

x²+1/x²=(2+√5)²+1/(2+√5)²

          =(4+4√5+5)+1/(4+4√5+5)

          =9+4√5 + 1/(9+4√5)

          =9+4√5 +1(9-4√5)/(9+4√5)(9-4√5)                [Rationalize]

          =9+4√5 + (9-4√5)/(9²-[4√5]²)

          =9+4√5 + (9-4√5)/1

          =9+4√5+9-4√5

          =18