What is the value of a?

Algebra Level 3

If a ∈ ( 0 , 1 ) a \in (0,1) is a real root of the equation x 3 − 3 x 2 − 3 x + 1 3 = 0 x^3-\sqrt 3x^2-3x+\dfrac 1{\sqrt 3} =0 , then what is the value of 10 a − 3 10a-\sqrt 3 ?


The answer is 0.031.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Tom Engelsman
Aug 15, 2019

There are actually 3 distinct real roots: x = − 1.19175 , 0.176327 , 2.74748 x = -1.19175, 0.176327, 2.74748 . You may want to be more specific in the desired final computation......only have a 1-in-3 chance of being correct in the current problem statement!

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Oh, I have overlooked it. Modifying the problem. Thanks.

A Former Brilliant Member - 1 year, 10 months ago

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No prob....have a great day!

tom engelsman - 1 year, 10 months ago

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