Question

If a =9 - 4 √5 , find the value of [a -1/a]²​

Answer 1

HEY USER !!

HERE IS UR ANSWER ---

Given ,,

x = 9 - 4√5

1/x = 1/ 9 - 4√5

So, firstly we hv to rationalize the denominator of 1/x.

( 1 / 9 - 4√5 ) × ( 9 + 4√5 / 9 + 4√5)

= 9 + 4√5 / ( 9 )^2 - (4√5)^2

= 9 + 4√5 / 81 - 80

= 9 + 4√5 / 1

= 9 + 4√5

So , we hv to find x - 1/x....

x = 9 - 4√5

1/x = 9 + 4√5

= 9 - 4√5 - ( 9 + 4√5)

= 9 - 4√5 - 9 - 4√5

= - 8√5

HOPE IT HELPS...