Question

if x^2-5x+1=0 then find the value of x+1/x

Answer 1

Given:

A quadratic equation

${x}^{2} - 5x + 1 = 0$

To find:

The value of x + 1/x.

Solution:

The value of x + 1/x is 5.

To answer this question, we need to follow the following steps:

As we know in a quadratic equation,

$a {x}^{2} + bx + c = 0$

a, b and c are called coefficients.

a and b are coefficients of x2 and x respectively.

Now,

As given, we have a quadratic equation,

${x}^{2} - 5x + 1 = 0$

The above equation can be written as

${x}^{2} + 1 = 5x$

After dividing the above equation by 'x' on both sides, we get

$x + \frac{1}{x} = 5$

Hence, the value of x + 1/x is 5.

Answer 2

Answer:

The value of $x+ \frac{1}{x}$ is 5.

Step-by-step explanation:

In context to the question asked,

We have to find of $x+ \frac{1}{x}$,

As per the data given in the question,

It is given that,

$x^2-5x+1=0$

Now, by shifting $-5x$ on the right side we get

=> $x^2 +1=5x$

Now, divide both sides by $x$ we get

$=> x+ \frac{1}{x} = 5$

Hence, the required solution is 5.