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

Answers ( )

    0
    2021-08-14T08:20:22+00:00

    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
    0
    2021-08-14T08:20:22+00:00

    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 , 35/2.

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

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