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Thread: U-Substitution

  1. #1
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    U-Substitution

    Hello Everybody,

    I'm really struggling with this following 3-part problem. Any help or guidance through them would be greatly appreciated.

    1a. Using u-substitution, solve (x^2 - 2)^2 - 3(x^2 - 2) - 4 = 0.

    So I was able to figure this problem out using u-substitution and got x = (±) square root of 6 & x = ±1.

    1b. The quadratic formula solves equations of the form ax^2 + bx + c = 0. Find the formula that solves a(x^2 - d)^2 + b(x^2 - d) + c = 0

    For this problem, their looking for a formula but I'm not sure which one or how to find it.

    1c. Use your formula from part (b) to verify your answers from part (a).

    For this last part, part 1b must be completed.

  2. #2
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    Quote Originally Posted by noahpww View Post
    Hello Everybody,

    I'm really struggling with this following 3-part problem. Any help or guidance through them would be greatly appreciated.

    1a. Using u-substitution, solve (x^2 - 2)^2 - 3(x^2 - 2) - 4 = 0. use u = x^2 - 2

    So I was able to figure this problem out using u-substitution and got x = (±) square root of 6 & x = ±1.

    1b. The quadratic formula solves equations of the form ax^2 + bx + c = 0. Find the formula that solves a(x^2 - d)^2 + b(x^2 - d) + c = 0

    For this problem, their looking for a formula but I'm not sure which one or how to find it. use u = x^2 - d

    1c. Use your formula from part (b) to verify your answers from part (a).

    For this last part, part 1b must be completed.
    .
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
    Senior Member
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    Quote Originally Posted by noahpww View Post
    Hello Everybody,


    I'm struggling with this 3-part problem. Any help or suggestions would be greatly appreciated!


    1a. Using u-substitution, solve (x^2 - 2)^2 - 3(x^2 - 2) - 4 = 0.


    I was able to solve this problem using u-substitution and got x = (±) the square root of 6 & x = ±1. You really should say which substitution you made since if you made a mistake we would not be able to help you. Having said that, you used u=x2-2 and got the correct answers. Good for you.


    1b. The quadratic formula solves equations of the form ax^2 + bx + c = 0. Find the formula that solves a(x^2 - d)^2 + b(x^2 - d) + c = 0. Let u = x2-d and do exactly what you did above. You'll have d instead of 2


    This one asks for a formula but I'm not sure which one and how to find it.


    1c. Use your formula from part (b) to verify your answers from part (a).

    Now that you have x solved for in terms of d, so plug in 2 for d and you'll get the same answers as in part a.


    This final part requires part 1b to be completed first.
    See red above
    A mathematician is a blind man in a dark room looking for a black cat which isn’t there. - Charles R. Darwin

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