Question

If x+1/x=17/4 then what is the value of x

Answer 1

x+1/x=17/4

x+1=17x/4

4x+4=17x

4x-17x=-4

-13x=-4

x=-4/-13=4/13

Answer 2

Given

$x+\dfrac{1}{x}=\dfrac{17}{4}$

To find

The value of x = ?

Solving,

$x+\dfrac{1}{x}=\dfrac{17}{4}$

$\implies \dfrac{x^{2} +1}{x} = \dfrac{17}{4}$

$\implies 4x^{2} +4=17x$

$\implies 4x^{2} -17x+4=0$

$\implies 4x^{2} -x-16x+4=0$

$\implies x(4x-1)-4(4x-1)=0$

$\implies (x-4)(4x-1) = 0$

Now,

$x-4 = 0\\\implies x = 4$

$4x-1=0$

$\implies x = \dfrac{1}{4}$

$\boxed{\boxed{\bold{Therefore, \ there \ are \ 2 \ values \ of \ x: \ 4 \ and \ \frac{1}{4}}}}}}$