Question

1/x+x/2=11/6 transformable to quadratic equations​

Answer 1

Note: Consider we need to find the solution of given equation.

Given:

The equation is

$\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}$

To find:

The solution of the equation.

Solution:

We have,

$\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}$

$\dfrac{2+x^2}{2x}=\dfrac{11}{6}$

By cross multiplication, we get

$6(2+x^2)=11(2x)$

$12+6x^2=22x$

$6x^2-22x+12=0$

$2(3x^2-11x+6)=0$

Divide both sides by 2.

$3x^2-11x+6=0$

Splitting the middle term, we get

$3x^2-9x-2x+6=0$

$3x(x-3)-2(x-3)=0$

$(x-3)(3x-2)=0$

Using zero product property, we get

$x-3=0$ and $3x-2=0$

$x=3$ and $x=\dfrac{2}{3}$

Therefore, the solutions of the given equation are $x=3$ and $x=\dfrac{2}{3}$.