Quadratic equation formula, where did I go wrong?

The question is, find the value of u using the quadratic formula

u + 1 + 3/(u + 1) = 8

u(u + 1) + u + 1 + 3 = 8(u + 1)

u^2 + u + u + 1 + 3 = 8u + 8

u^2 + 2u + 4 = 8u + 8

....subtracting 2u and 4 from both sides...

u^2 = 6u + 4

..subtracting 6u and 4 from both sides...

u^2 - 6u - 4 = 0

Using the formula....

[-(-6) +/- √(-6)^2 - 4 x 1 x (-4)] / 2 x 1

[6 +/- √36 +16] / 2

[6 +/- √52] / 2

so...

(6 + 7.211) / 2 = 6.61 = u

or (6 - 7.211) / 2 = -0.61 = u

But this is wrong! Where did I go wrong? Thanks

5 Answers

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  • 2 years ago
    Favorite Answer

    I changed the negative answer to 4 places, and then it passes OK.

    u = 6.61, – 0.6055

    just check the answers

    check

    u + 1 + 3/(u + 1) = 8

    7.61 + 3/7.61 = 8

    8.00 = 8

    ok

    – 0.6055 + 1 + 3/(– 0.6055 + 1) = 8

    0.3945 + 3/0.3945 = 8

    7.999=8

    ok

  • Como
    Lv 7
    2 years ago

    u + 1 + 3(u + 1) = 8

    u + 1 + 3u + 3 = 8

    4u = 4

    u = 1

  • 2 years ago

    .

    u + 1 + 3/(u + 1) = 8

    multiply both sides of the equation by u + 1;

    (u + 1)(u + 1) + 3 = 8(u + 1)

    then simplify

    u² + 2u + 1 + 3 = 8u + 8

    u² - 6u - 4 = 0

    complete the square or use the quadratic formula

    (u - 3)² = 4 + 9

    (u - 3)² = 13

    u - 3 = ±√13

    u = 3 ± √13

    ━━━━━

  • Anonymous
    2 years ago

    You didn't do anything wrong. Plugging back into the original equation, you'll see that it checks out. Perhaps they want the exact radical solution, or perhaps they want you to round to a certain decimal place.

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  • (u + 1) + 3 / (u + 1) = 8

    I'd let u + 1 = k and go from there

    k + 3/k = 8

    k^2 + 3 = 8k

    k^2 - 8k + 3 = 0

    k = (8 +/- sqrt(64 - 12)) / 2

    k = (8 +/- sqrt(52)) / 2

    k = (8 +/- 2 * sqrt(13)) / 2

    k = 4 +/- sqrt(13)

    u + 1 = 4 +/- sqrt(13)

    u = 3 +/- sqrt(13)

    u = 3 + sqrt(13) , 3 - sqrt(13)

    You went wrong in your final step. Maybe you shouldn't round it off. Just give it to them in a radical form.

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