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

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anonymous
  • anonymous
Wait no. I'm sorry give me a second
anonymous
  • anonymous
Sorry! it was originally correct, but what happened to the 30?
campbell_st
  • campbell_st
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
campbell_st
  • campbell_st
oops should read \[10([u - 3] + 30)\]
anonymous
  • anonymous
Okay I get it now! And the answer is u^2-10u+21?
campbell_st
  • campbell_st
well you have on the right side 10[u -3] + 30) = 10(u + 27) = 10u + 270 you can check to make sure
anonymous
  • anonymous
woah.. you lost me now
campbell_st
  • campbell_st
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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