Question

6.If x=9+4sqrt(5) find the value of x-1/x .​

Answer 1

Answer:

Hey mate! Here's your answer:

Step-by-step explanation:

x = 9 + 4√5.

To find: x - 1/x.

(9 + 4√5) - (1 / 9 + 4√5)

(1 / 9 + 4√5) can be rationalised.

(1 / 9 + 4√5) * (9 - 4√5 / 9 - 4√5)

9 - 4√5 / 9² - (4√5)²

9 - 4√5 / 81 - 80

9 - 4√5.

Now,

x = 9 + 4√5 and 1/x = 9 - 4√5.

So x - 1/x = (9 + 4√5) - (9 - 4√5).

9 + 4√5 - 9 + 4√5

4√5 + 4√5

8√5.

So when x = 9 + 4√5, x - 1/x = 8√5.

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