Question

if x = 2+root5 ,find the value of x2+1/x2=18​

Answer 1

Answer:

x=2+√5

x^2=(2+√5)^2

     =(2)^2+2*2*√5+(√5)^2

     =4+4√5+5

     =9+4√5

1/x^2=1/9+4√5

        =1/9+4√5*9-4√5/9-4√5

        =9-4√5/(9)^2-(4√5)^2

        =9-4√5/81-16*5

        =9-4√5/81-80

        =9-4√5

now,    x^2+1/x^2=9+4√5+(9-4√5)

                           =9+4√5+9-4√5

                           =9+9+4√5-4√5

                           =18 ans      

Step-by-step explanation:

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