anonymous
  • anonymous
solve x^4-34x^2=-225
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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apoorvk
  • apoorvk
let x^2 be t then the eqn. becomes: t^2-34t+225=0 now solve the quadratic and get values of t, and eliminate nay negative values of t, since t is x^2, which cannot be negative.
anonymous
  • anonymous
\[x ^{4}-34x ^{2}=-225\]First, let's set this equal to 0. \[x ^{4}-34x ^{2}+225=0\] From there, examine the terms and identify it as being quadratic-like because it has three terms that mimic a quadratic (as the power of x on the second term is half the power of x on the first term, and the third term has no x). Then, as others have said, we want to make a substitution: \[u=x ^{2}\] In order to sub it in for the first term, we can do a little re-write first. \[(x ^{2})^2-34x ^{2}+225=0\] Now you can sub it in: \[(u)^2-34(u)+225=0\] Now, factor like usual: \[(u-25)(u-9)=0\] And then use the Zero-Product Property: \[u-25=0\] \[u-9=0\]Solve for u u = 9 and u = 25 At this point, don't forget, you were solving for x to begin with, so now you have to substitute back. \[u=x ^{2}\]Therefore: \[x ^{2}=9\]and \[x ^{2}=25\] To solve for x, take the square root of both sides for each equation. \[\sqrt{x ^{2}}=\pm \sqrt{9}\]\[x=\pm3\] and \[\sqrt{x ^{2}}=\pm \sqrt{25}\]\[x=\pm5\]

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