Question

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

Answer 1

x = 9 - 4 √5.

Since (a+b)(a - b) = a^2 - b^2

(9 - 4 √5)(9 + 4 √5) = 81 - 80 = 1

=>9 - 4 √5 = 1/(9 +4 √5) which is ‘x’

Therefore we can write 1/x = 9 + 4 √5

=> x + 1/x = (9 - 4 √5) + (9 + 4 √5) = 9 + 9 = 18.