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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 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.
Mar
23
answered finding the local extremum of a function of 2 variables
Mar
22
answered Prove that $\sqrt{3}+ \sqrt{5}+ \sqrt{7}$ is irrational
Mar
19
answered Why if we have more vectors than rows can the vectors not be linearly independent?