Question

Can someone do question 4 for me with step by step instructions

Answer 1

Given that

`x + (1)/(x) = 9`

[Square both sides]

`(x + (1)/(x))^2 = 9^2`

The Algebraic Formula:

`(a+b)^2 = a^2 + 2(a)(b) + b^2`
Therefore:

`x^2 + 2(x)((1)/(x)) + ( (1)/(x))^2 = 9^2`

[Evaluate the terms]

`x^2 + 2+ (1)/(x^2) = 81`

[-2 on both sides]

`x^2 + (1)/(x^2) = 81 -2`

[Evaluate the right side]

`x^2 + (1)/(x^2) = 79` (Answer B)