Question

x +1/x =41/20
Solve for x by factorisation

Answer 1

ANSWER:

Given:

• x + 1/x = 41/20

To Find:

• Value of x

Solution:

We are given that,

$\implies x+\dfrac{1}{x}=\dfrac{41}{20}$

Taking LCM,

$\implies \dfrac{x^2+1}{x}=\dfrac{41}{20}$

On cross-multiplying,

$\implies 20(x^2+1)=41x$

$\implies 20x^2+20=41x$

Transposing 41x to LHS,

$\implies 20x^2-41x+20=0$

On splitting the middle term,

$\implies 20x^2-41x+20=0$

$\implies 20x^2-25x-16x+20=0$

$\implies 5x(4x-5)-4(4x-5)=0$

$\implies (5x-4)(4x-5)=0$

So,

$\implies\bf x=\dfrac{4}{5},\:\:\dfrac{5}{4}$