(adsbygoogle = window.adsbygoogle || []).push({}); 1) Prove that 45 degrees can be trisected with straightedge and compass.

My attempt:

60 deg constructible since equilateral triangle constructible

and 45 deg constructible since 90 deg constructible and we can bisect any angle.

=>(60-15)=15 deg constructible

Then copy this angle 3 times to trisect 45 deg (fact: any angle can be copied with straightedge and compass)

Did I get the right idea?

2) Let F={a+b√3 | a,b E Q(√2)} where Q(√2)={c+d√2 | c,d E Q}. Show that every element of F is the root of a polynomial of degree 4 with rational coefficients.

No clue...how to begin?

Can someone please help me? Particularly with Q2. Thanks a lot!

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# Straightedge and compass constructions

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