Question

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Answer 1

Answer :

Option (1) - 0.

Explanation : 

Given x + 1/x = 5

On Squaring both sides, we get

(x + 1/x)^2 = (5)^2

We know that (a+b)^2 = a^2 + b^2 + 2ab

Where a = x, b = 1/x.

Then (x + 1/x)^2 = (5)^2

         x^2 + 1/x^2 + 2 * x * 1/x = 25

         x^2 + 1/x^2 + 2 = 25

        x^2 + 1/x^2 = 25 - 2

        x^2 + 1/x^2 = 23.       -------------- (1)




Given x + 1/x = 5

On cubing both sides, we get

(x + 1/x)^3 = (5)^3

We know that (a+b)^3 = a^3 + b^3 + 2ab(a+b)

(x + 1/x)^3 = (5)^3

x^3 + 1/x^3 + 2x * 1/x(x + 1/x) = 125

x^3 + 1/x^3 + 2(5) = 125

x^3 + 1/x^3 = 125 - 10

x^3 + 1/x^3 = 110        ------------ (2)



Now, (x^3 + 1/x^3) - 5(x^2 + 1/x^2)  + (x + 1/x)

         = 110 - 5(23) + 5

         = 110 - 115 + 5

         = -5 + 5

         = 0.


Hope this helps!