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Let p, q E Z be distinct primes. Prove that Q(YP,that QC Q(Vp+ Vq) is a degree 4 extension.) = Q(YP + Vq), and

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Abstract Algebra. Answer in detail please.

Let p, q E Z be distinct primes. Prove that Q(YP,
that QC Q(Vp+ Vq) is a degree 4 extension.
) = Q(YP + Vq), and
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Let p, q E Z be distinct primes. Prove that Q(YP, that QC Q(Vp+ Vq) is a degree 4 extension. ) = Q(YP + Vq), and

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Step 1

To prove the statements about the given field extensions, (two quadratic and one 4th degree over Q)

Step 2

Required to prove statements 1) and 2). Note that 2) follows immediately from 1) once we show deg K =4 

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Step 3

1) Proof that K is co...

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