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α^4 + β^4 Expansion?
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DaftPunk327
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#1
I need to expand [α^4 + β^4 ] in terms of α + β and αβ
but unfortunately my textbook doesn't cover this
but unfortunately my textbook doesn't cover this
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james22
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#2
DaftPunk327
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#3
(Original post by james22)
Start with (a+b)^4.
Start with (a+b)^4.
that's what I did originally, but I ended up with 5 terms, and trying to simplify them all in terms of α + β and αβ became too much of a headache
I'm pretty sure there's a way to do it using α^2 + β^2 but I've got no idea what it is
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james22
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#4
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#4
(Original post by DaftPunk327)
that's what I did originally, but I ended up with 5 terms, and trying to simplify them all in terms of α + β and αβ became too much of a headache
I'm pretty sure there's a way to do it using α^2 + β^2 but I've got no idea what it is
that's what I did originally, but I ended up with 5 terms, and trying to simplify them all in terms of α + β and αβ became too much of a headache
I'm pretty sure there's a way to do it using α^2 + β^2 but I've got no idea what it is
When you expans (a+b)^4 you should be able to write it in terms of a^4+b^4, ab and another term which you need another trick for.
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DaftPunk327
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#5
(Original post by james22)
You also have to use (a+b)^2, but not yet.
When you expans (a+b)^4 you should be able to write it in terms of a^4+b^4, ab and another term which you need another trick for.
You also have to use (a+b)^2, but not yet.
When you expans (a+b)^4 you should be able to write it in terms of a^4+b^4, ab and another term which you need another trick for.
so I'm getting:
a^2 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4
(a^4+b^4) + 6(ab)^2 + 4ab(a^2+b^2)
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james22
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#6
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#6
(Original post by DaftPunk327)
okay
so I'm getting:
a^2 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4
(a^4+b^4) + 6(ab)^2 + 4ab(a^2+b^2)
okay
so I'm getting:
a^2 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4
(a^4+b^4) + 6(ab)^2 + 4ab(a^2+b^2)
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