Evaluate expression W/O Calculator

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The discussion focuses on finding the exact value of the expression √[3]{10+6√3} + √[3]{10-6√3}. Participants suggest letting x equal the expression and finding x^3, leading to the equation x^3 + 6x - 20 = 0. Through the Rational Root Theorem, they identify that the only real solution is x = 2. The conversation highlights the use of binomial expansion and factoring techniques to simplify the problem. Ultimately, the exact value of the expression is confirmed to be 2.
  • #31
S.R said:
I didn't notice that; thanks!

x^3-6x-20=0

(x-2)(x^2+2x+10) = 0

The only real solution is x=2.

Yeah, well done! :approve:

EDIT: Small correction: the equation should've been x^3 + 6x - 20 = 0. Small matter, just a typo. :smile:
 

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