Question

if x=9-4√5,then find the value of x^2+1/x^2

Answer 1

x=9-4√5

1 =     1   
x    9-4√5

Rationalising the equation

1 =     1   × 9+4√5
x    9-4√5  9+4√5

1  = 9+4√5
x     81-80

1 = 9+4√5
x

x²=(9-4√5)² = 81+80 - 72√5

1 = (9+4√5)²= 81+80+72√5
x²

x²+1/x² = 161-72√5+161+72√5

x²+1/x² = 161+161

x²+1/x²=322

Answer 2

so given x = 9 - 4√5
             1/x = 1/(9 - 4√5)
                  =   9 + 4√5 after rationalizing
     so we know (a+b)² + (a-b)² = 2(a² + b²)
                                            so substituting the values
                            = 2(81 + 80)
                             = 2 x 161 = 322 ANSWER