Question

x+1/x=10/3 solved by quadratic equation

Answer 1

Answer:

Step-by-step explanation:

x+1/x  

that equals 10/3

times by 3x (lcm)

so 3x squared + 3 = 10x

3x squared-10x+3=0

(3x -1) (x-3)

x= 1/3 or 3

Answer 2

To solve it by quadratic equation, the actual solution is given below.

$\begin{aligned}&x+\dfrac{1}{x}=\dfrac{10}{3}\\ \\ \implies\ \ &\dfrac{x^2+1}{x}=\dfrac{10}{3}\\ \\ \implies\ \ &3(x^2+1)=10x\\ \\ \implies\ \ &3x^2-10x+3=0\end{aligned}$

Now we got a quadratic equation. This is going to be solved by the application of quadratic formula.

Let,

$a=3\quad;\quad b=-10\quad\quad c=3$

Discriminant equals,

$b^2-4ac=100-36=64$

Now,

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\ =\ \dfrac{10\pm8}{6}\ =\ \large\boxed{\mathbf{3}\quad\text{OR}\quad\mathbf{\dfrac{1}{3}}}$