Math, asked by 1020janvikv42020, 7 months ago

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

Answers

Answered by RISH4BH
81

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

Answered by CopyThat
27

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
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