polynomial equations

label Algebra
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49 - (x 2 - 3) = x 4 - 6x 2 + 9

Which of the following equations is equivalent to the equation above, if z = x 2 - 3?

Jun 18th, 2015

Thank you for the opportunity to help you with your question! I'll show you step by stp.

40 - (x^2 - 3) = x^4 - 6x^2 + 9

z = x^2 - 3, then equation becomes

49 - z = x^4 - 6x^2 + 9

49 - z = (x^2 - 3)^2 (factored)

49 - z = z^2

z^2+ z - 49 = 0

This is the final equation when z=x^2 - 3


Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 18th, 2015

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