What's the Second Part?Date: 21 Mar 1995 01:29:45 -0500 From: peter eckersley Subject: help The question: If x = root3 + root2, show that x^4 - 10x^2 + 1 = 0. Hence prove that root3 + root2 is irrational. The first part is ok by substitution. The second part... ? Peter Eckersley Valley View Secondary School Date: 21 Mar 1995 10:11:13 -0500 From: Dr. Ken Subject: Re: help Hello there! Well, here are two things I'd tell you about this: a) Use the quadratic formula on the quartic equation, and use x^2 as your variable. So you get x^2 = (10 +- Sqrt{100 - 4})/2, and then simplify. What does this information about x^2 tell you about x? b) I wonder whether the person writing the question really meant to say "Hence prove that root3 + root2 is algebraic." Because if you can find a polynomial that has the number in question as a root, you've just satisfied the definition of algebraic. I hope this helps! -Ken "Dr." Math |
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