Question

7. If x= (2+V5), find the value of x² +​

Answer 1

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Answer 2

Answer:

x = 2+root5

x2 = (2+root5)2 =9 +4root5 {using identity (a+b)2}

1/x2  = (1/2+root5 )2  =1/9 +4root5 

so x2 +1/x2    = 9+4root5 + 1/9+4root5

                     =9+4root5 + 9- 4 root5 

                                         (9)2  - (4root5)2

                     =9 +4root5 +9 -4root5 

                                            1

                    9+4root5 +9 - 4root5  =18

thus x2 +1/x2 =18 proved