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

Question

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

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1 month 2021-08-14T08:18:56+00:00 2 Answers 0 views 0

• 3 + √5/2
• 3 – √5/2

### Given

• x + 1/x = 3 , x ≠ 0

• Roots

### Solution

• x + 1/x = 3

(Multiply x on both sides)

• x² + 1 = 3x
• x² – 3x + 1 = 0

• 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
2. ## Given:

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

## ToFind:

• 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

=> x = -(-3) ± √(-3)²-4×1×1/2×1

=> x = 3± √ 9-4/2.

=> x = 3 ± √5 / 2.

=> x = 3+5/2 , 35/2.

Hence the required answer is 3+5/2 , 35/2