Question

X+1/X=41/20 split the middle term​

Answer 1

Answer:

how

Step-by-step explanation:

OK thank you do much and like my answer

Answer 2

Answer:

The roots of the given quadratic equation are

$\displaystyle{\boxed{\red{\sf\:x\:=\:\dfrac{5}{4}}}}\sf\:\quad\:OR\:\quad\:{\boxed{\red{\sf\:x\:=\:\dfrac{4}{5}}}}$

Step-by-step-explanation:

The given equation is

$\displaystyle{\sf\:x\:+\:\dfrac{1}{x}\:=\:\dfrac{41}{20}}$

We have to find the roots of the given equation by splitting the middle term.

Now,

$\displaystyle{\sf\:x\:+\:\dfrac{1}{x}\:=\:\dfrac{41}{20}}$

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

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

$\displaystyle{\implies\sf\:20\:\times\:(\:x^2\:+\:1\:)\:=\:41x}$

$\displaystyle{\implies\sf\:20\:x^2\:+\:20\:=\:41\:x}$

$\displaystyle{\implies\sf\:20\:x^2\:+\:20\:-\:41\:x\:=\:0}$

$\displaystyle{\implies\sf\:20\:x^2\:-\:41\:x\:+\:20\:=\:0}$

$\displaystyle{\implies\sf\:20\:x^2\:-\:25\:x\:-\:16\:x\:+\:20\:=\:0}$

$\displaystyle{\implies\sf\:5x\:(\:4x\:-\:5\:)\:-\:4\:(\:4x\:-\:5\:)\:=\:0}$

$\displaystyle{\implies\sf\:(\:4x\:-\:5\:)\:(\:5x\:-\:4\:)\:=\:0}$

$\displaystyle{\implies\sf\:4x\:-\:5\:=\:0\:\quad\:OR\:\quad\:5x\:-\:4\:=\:0}$

$\displaystyle{\implies\sf\:4x\:=\:5\:\quad\:OR\:\quad\:5x\:=\:4}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:x\:=\:\dfrac{5}{4}}}}\sf\:\quad\:OR\:\quad\:\underline{\boxed{\red{\sf\:x\:=\:\dfrac{4}{5}}}}}$