Question

Find roots of quadratic equation x+1/x =3 where x is not equals to 0.​

Answer 1

Given:

• A Quadratic equation is given to us.
• The equation is x + 1 / x = 3.

To Find:

• The roots of quadratic equation.

Soluⁿ :

Given quadratic equation is , x + 1/x = 3

=> x + 1/x = 3.

=> x² + 1 / x = 3.

=> x² + 1 = 3x.

=> x² -3x + 1 = 0.

Now let's use quadratic formula ,

With respect to Standard form ax²+bx+c = 0.

• a = 1
• b = (-3)
• c = 1

$\large{\underline{\boxed{\red{\sf{\dag x = \dfrac{ -b \pm \sqrt{b^2-4ac}}{2a}}}}}}$

=> x = -(-3) ± √(-3)²-4×1×1/2×1

=> x = 3± √ 9-4/2.

=> x = 3 ± √5 / 2.

=> x = 3+√5/2 , 3-√5/2.

Hence the required answer is 3+√5/2 , 3-√5/2

Answer 2

Answer:

• 3 + √5/2
• 3 - √5/2

Step-by-step explanation:

Given

• x + 1/x = 3 , x ≠ 0

To find

• Roots

Solution

• x + 1/x = 3

(Multiply x on both sides)

• x² + 1 = 3x
• x² - 3x + 1 = 0

(Standard quadratic equation)

• x = -b±√b² - 4ac/2a

a = 1 , b = -3 , c = 1

b² - 4ac = 9 - 4 = 5

• x = 3 ± √5/2

Hence, the roots are:

• 3 + √5/2
• 3 - √5/2