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Algebra Level 3

What is the algebraic conjugate of 657 − 4355 \sqrt{657} - 4355 ?

4355 + 657 \sqrt{4355}+657 − 657 − 4355 -\sqrt{657}-4355 4355 − 657 \sqrt{4355} - \sqrt{657} 657 + 4355 \sqrt{657}+4355 4355 + 657 \sqrt{4355} + \sqrt{657} 4355 + 657 4355 + 657

Jomari Ubas by Jomari Ubas , 26, Philippines

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1 solution

Jomari Ubas
Jan 29, 2015

The conjugate is where we change the sign in the middle of two terms.

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That is a simplistic understanding of conjugates, which isn't always true.

To find the algebraic conjugate of a real/complex number c c , we find the minimal polynomial f ( x ) f(x) such that f ( c ) = 0 f(c) = 0 . Then, the other roots of f ( x ) f(x) are known as it's algebraic conjugates. This would depend on the field that you're working with, which is often assumed to be the rational numbers.

I have updated the answer to − 657 − 4355 - \sqrt{ 657 } - 4355 .

Calvin Lin Staff - 6 years, 4 months ago

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