Algebra Galore 3

Algebra Level 1

What is the conjugate of 5 − 30 5-\sqrt{30} ?

30 − 5 \sqrt{30}-5 None of the above 5 + 30 5+\sqrt{30} 5 − 30 \sqrt{5}-30

Alex Segesta by Alex Segesta , 20, USA

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1 solution

The conjugate of x + y x+y is x − y x-y . In this case, x = 5 x=5 and y = − 30 y=-\sqrt{30} , so the conjugate must be 5 + 30 \boxed{5+\sqrt{30}} .

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The proper definition of a conjugate comes from field theory, where the conjugate elements are all the roots of the minimal polynomial.

In this case, if 5 − 30 5 - \sqrt{30} is a root of a polynomial with integer coefficients, then so is 5 + 30 5 + \sqrt{30} . Hence, these elements are conjugates of each other.

Calvin Lin Staff - 4 years, 2 months ago

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