Using the Baudhāyana–Pythagoras Theorem, equal chords with equal radii give equal perpendicular distances from the centre. Hence, chords of equal length are always equidistant from the centre of the circle.
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Rearranging the conditional constraint gives x – 2y – 6 = 0. The polynomial can be formatted as x cube + (-2y) cube + (-6) cube – 3(x)(-2y)(-6), which evaluates directly to 0 because the base sum is 0.
The expression matches the identity form of a cube + b cube + c cube – 3abc where a = x, b = y and c = 4. Since the sum a + b + c equals 0, the entire ...
Factoring n cube – n gives the expression (n – 1)(n)(n + 1), which represents three consecutive integers. In any three consecutive numbers, at least one is a multiple of 2 and one is a multiple of 3.
We first find a square + b square + c square by expanding (a + b + c) square, which equals 5. Substituting these evaluated numerical components into the standard three-variable cubic identity gives minus 25.