Question

Please solve the sum in the question

Answer 1

`\displaystyle\\Answer:\ x^2+(1)/(x^2)=5`

Explanation:

`\displaystyle\\(x-(1)/(x) )=√(3) \\`

Let's square both parts of the equation:

`\displaystyle\\(x-(1)/(x) )^2=(√(3))^2 \\(x)^2-2*x*(1)/(x) +((1)/(x))^2 =3\\x^2-2*1+(1)/(x^2)=3\\ x^2-2+(1)/(x^2)+2 =3+2\\x^2+(1)/(x^2)=5`

Answer 2

x² +
`(1)/(x^2)` = 5

Explanation:

using the identity

(a - b)² = a² + b² - 2ab , then given

(x -
`(1)/(x)` ) =
`√(3)` ( square both sides )

(x -
`(1)/(x)` )² = (
`√(3)` )² , that is using the above identity

x² +
`(1)/(x^2)` - 2(x ×
`(1)/(x)` ) = 3

x² +
`(1)/(x^2)` - 2(1) = 3

x² +
`(1)/(x^2)` - 2 = 3 ( add 2 to both sides )

x² +
`(1)/(x^2)` = 5