Question

 If x = 9 - 4 _/5 then find x + 1/x​

Answer 1

Answer:

103682

Explanation:

x = 9+4√5 ………………………(1)

And, 1/x = 1/( 9+4√5)

By rationalising the denominator

= (9–4√5 ) /(81–80)

1/x = 9–4√5 ……………………..(2)

Hence x + 1/x = 9+ 4√5 + 9 - 4√5 = 18 …………(3)

Since x² + (1/x)² = (x + 1/x)² - 2

=> x² + (1/x) ² = 18² -2 = 324 -2= 322 ………..(4)

Now, x^4 + (1/x)^4

= (x² + 1/x² )² -2

= (322)² -2

= 103684 - 2

= 103682 ……….ANS

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