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anonymous

  • one year ago

Let u = x^2+ 3. Which equation is equivalent to (x^2+3)^2+ 21 = 10x^2+ 30 in terms of u?

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  1. campbell_st
    • one year ago
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    well factor the right hand side of the equation and you get \[(x^2 + 3)^2 + 21 = 10(x^2 + 3)\] since \[u = x^2 + 3\] the equation becomes \[(u)^2 + 21 = 10(u)\] now just simplify

  2. anonymous
    • one year ago
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    Wait I typed in the equation incorrectly. I'm sorry. It was: Let u = x^2+ 3. (x^2+3)^2+ 21 = 10(x^2+ 30)

  3. anonymous
    • one year ago
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    @campbell_st

  4. anonymous
    • one year ago
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    Wait no. I'm sorry give me a second

  5. anonymous
    • one year ago
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    Sorry! it was originally correct, but what happened to the 30?

  6. campbell_st
    • one year ago
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    ok then so the left side is straight forward rewrite \[u = x^2 + 3~~~as~~~ x^2 = u - 3\] so the right side becomes \[10(x^2 + 30) = 10([u^2 - 3] + 30)\] hope that helps

  7. campbell_st
    • one year ago
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    oops should read \[10([u - 3] + 30)\]

  8. anonymous
    • one year ago
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    Okay I get it now! And the answer is u^2-10u+21?

  9. campbell_st
    • one year ago
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    well you have on the right side 10[u -3] + 30) = 10(u + 27) = 10u + 270 you can check to make sure

  10. anonymous
    • one year ago
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    woah.. you lost me now

  11. campbell_st
    • one year ago
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    the problem becomes \[u^2 + 21 = 10([u - 3] + 30) ~~~or~~~~u^2 + 21 = 10(u + 27)\] so distribute and collect like terms.

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