Question

the sum of a number and it's reciprocal is 3, find the number using quadratic equations​

Answer 1

Step-by-step explanation:

(x²+x ) / x -3

x² + x = 3x

x²-2x=0

x(x-2 ) =0

x=0 ( or) x=2

Answer 2

Given:

The sum of a number and its reciprocal is 3

To Find:

The number using quadratic equations​

Solution:

As we know that the reciprocal of a number a is 1/a

According to question

let us take the number be x

x+ 1/x = 3

(x² + 1)/x = 3 (Taking L.C.M)

x²+1 = 3x

x² - 3x + 1 = 0

Now, we will solve this quadratic equation for a,

Let us find the discriminant of the equation,

D = √(b²-4ac)

where b is the coefficient of x

            a is the coefficient of x²

           c is the constant

D = √((-3)²-4)

D = √5

Now the roots of the equation are

$x$= (-b±D)/2a

so,

$x_{1}$ = (-(-3)+√5))/2×1

$x_{1}$ =(3+√5)/2

$x_{2}$ = (3-√5)/2

Hence, the number is (3-√5)/2