Question

The sum of a number and twice it’s reciprocal is 11/3. Find the numbers

Answer 1

In order to find the answer you first write the statement of the question in an algebraic form. Just as follow:

`\begin{gathered} x+(2)/(x)=(11)/(3) \\ x^2+2=(11)/(3)x \\ x^2-(11)/(3)x+2=0 \end{gathered}`

Then, you obtained a quadratic equation. The general form of a quadratic equation is:

`ax^2+bx+c=0`

where a=1, b=-11/13 and c=2

The quadrativ formula is:

`x=(-b\pm√(b^2-4ac))/(2a)`

you replace:

`\begin{gathered} x=(-(11/3)\pm√((11/3)^2-4(1)(2)))/(2(1))=(-11/3\pm2.33)/(2) \\ x_1=-3 \\ x_2=0.66 \end{gathered}`