x^2=6x/(5-x) What is the sum of the roots of the above equation?

Question

x^2=6x/(5-x)
What is the sum of the roots of the above equation?

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Alice 2 weeks 2021-09-12T05:02:11+00:00 1 Answer 0

Answers ( )

    0
    2021-09-12T05:03:13+00:00

    Answer:

    x = 3 or x = 2 or x = 0 thus: 5

    Step-by-step explanation:

    Solve for x over the real numbers:

    x^2 = (6 x)/(5 – x)

    Cross multiply:

    x^2 (5 – x) = 6 x

    Expand out terms of the left hand side:

    5 x^2 – x^3 = 6 x

    Subtract 6 x from both sides:

    -x^3 + 5 x^2 – 6 x = 0

    The left hand side factors into a product with four terms:

    -x (x – 3) (x – 2) = 0

    Multiply both sides by -1:

    x (x – 3) (x – 2) = 0

    Split into three equations:

    x – 3 = 0 or x – 2 = 0 or x = 0

    Add 3 to both sides:

    x = 3 or x – 2 = 0 or x = 0

    Add 2 to both sides:

    Answer:  x = 3 or x = 2 or x = 0

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