#### Question

In the following, determine whether the given values are solutions of the given equation or not:

`x+1/x=13/6`, `x=5/6`, `x=4/3`

#### Solution

We have been given that,

`x+1/x=13/6`

`x+1/x-13/6=0`, `x=5/6`, `x=4/3`

Now if `x=5/6` is a solution of the equation then it should satisfy the equation.

So, substituting `x=5/6` in the equation, we get

`x+1/x-13/6`

`=5/6+(1/(5/6))-13/6`

`=5/6+6/5-13/6`

`=(25+36-65)/30`

`=(-4)/30`

Hence `x=5/6` is not a solution of the quadratic equation.

Also, if `x=4/3` is a solution of the equation then it should satisfy the equation.

So, substituting `x=4/3` in the equation, we get

`x+1/x-13/6`

`=4/3+(1/(4/3))-13/6`

`=4/3+3/4-13/6`

`=(16+9-26)/12`

`=(-1)/12`

Hence, `x=4/3` is not a solution of the quadratic equation.

Therefore, from the above results we find out that both `x=5/6` and `x=4/3` are not the solutions of the given quadratic equation.