Bill Kleinhans
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 Aug 22 comment Express roots in polynomials of equation $x^3+x^2-2x-1=0$ Use the fact that the discriminant is a perfect square. The field extension generated by one of the roots includes all the roots. Aug 18 comment Max volume of a cuboid given constraint Follows directly from the AM/GM inequality. Jul 31 answered How to distinguish between global maxima/minima and local maxima/minima of a function? May 31 answered Determining the max area of a trapezoid with no known sides May 26 comment Finding the largest triangle inscribed in the unit circle If the triangle is not equilateral, you can modify it to increase its area. So, if there is a triangle with maximum area, it must be equilateral. There are several optimization problems that have this subtlety. For example, the proof that the figure with maximum area for fixed perimeter is a circle. May 25 comment Finding the largest triangle inscribed in the unit circle You initially showed that the triangle must be isosceles with respect to any side. Isn't that enough? May 2 comment Find a second root of $x^3+px+q$ given the first root There is really no reason to provide the discriminate, unless it is a perfect square. Is the square root of the discriminant specified rational? Because in that case the field extension generated by any one of the roots is the root field. The other two roots would be in this field, and they can be expressed as linear combinations of 1, the original root, and the square of this root. Apr 26 answered Technique for proving four given points to be concyclic? Apr 21 awarded Yearling Apr 11 answered If $A+B=\pi/3$ then what will maximum value of $\tan(A).\tan(B)$? Apr 8 comment Prove if $7\mid a^2+b^2 \longrightarrow 7\mid a$ and $7\mid b$ Fermat's theorem on sums of two squares. Apr 7 answered Can ratios similar to those related to the surface area of a circle and sphere be applied to determine properties of a 3-sphere? Apr 6 answered How to maximize shipping box volume Mar 26 comment Finding the dimensions of a cuboid for minimal surface area The arithmetic mean is greater or equal to the geometric mean, with equality if and only if all the quantities being averaged are equal. Very powerful, since it often gives an absolute maximum or minimum. Mar 26 answered Determining points on a 3-dimensional intersection closest to the origin Mar 25 comment Homework Problem About Finding a Value of $k$ for Which the Given System of Equations Has No Solutions Make the two lines parallel. Mar 25 answered Finding the dimensions of a cuboid for minimal surface area Mar 24 answered Average of square roots's sum vs. square root of an average Mar 24 answered Find rational points on $x^2 + y^2 = 3$ and on $x^2 + y^2 = 17$ Mar 24 comment Prove that $\sqrt{3}+ \sqrt{5}+ \sqrt{7}$ is irrational In this case, the Galois transformations involve changing the signs of any or all of the roots of the three primes. Total of eight transformations, including unity. Your suggestion is not included.