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I can do all the question apart from the 'Conclude rt(2) in an element of Q(rt(2) + rt(3))'

That's all I need help on.

I tried

rt(2) = a + b(rt(2) + rt(3))

squaring it and equating you get

2 = a^{2}+ 5b^{2}+ (some other terms of rt(2) rt(3) rt(5))

but this cannot be true for a, b in Q, how else are you supposed to do this?

Thanks

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# Homework Help: Field extensions, proving an element is in a field

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