Finding Minimum from a completion of a square

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The discussion focuses on completing the square for the quadratic expression x^2 + 4x - 1, resulting in (x+2)^2 - 5, which indicates the minimum value is -5 at x = -2. Participants also discuss factoring the cubic equation 2x^3 + 3x^2 - 8x - 12 = 0, successfully identifying the factors as (x-2)(x+2)(2x+3). The conversation shifts to factoring the quartic equation x^4 - 3x^2 - 10 = 0, where a substitution simplifies it to a quadratic form. Lastly, they tackle expressing the function √3sin(2t) - 3cos(2t) in a specific form, leading to a system of equations to solve for parameters a and α, with ongoing clarification about the relationships between the terms. The thread emphasizes the importance of careful reading and understanding of mathematical principles.
  • #51
after all this 50 some post...look at the progression...

\sqrt{3}\sin{2t} - 3\cos{2t} = -\frac{\pi}{3}

seems to me that this is gettin further away from the answer...
 
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  • #52
Seems to me that you have not carefully read everything which has been said. The -pi/3 was a solution for alpha, not for the RHS in general.
 

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