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16 kwi 2024 · Identities VIII. Last updated at April 16, 2024 by Teachoo. Identity VII is. a 3 + b 3 + c 3 − 3abc = (a + b + c) (a 2 + b 2 + c 2 − ab − bc − ac) Lets take an example.
8 mar 2008 · In summary, the conversation discusses the geometrical significance of the equation a3 + b3 = c3, where a, b, and c are constants. Some suggest using the Pythagorean theorem with area instead of length, while others mention cubes and spheres in geometry.
1 kwi 2011 · It can be useful to first identify the pattern or relationship between the terms in the equation. Then, look for a math identity that matches that pattern. It can also be helpful to simplify the equation as much as possible before applying a math identity.
21 lip 2020 · The formula for (a+b+c)³ is a³ + b³ + c³ + 3a²b + 3ab² + 3ac² + 3bc² + 6abc. This is a generalization of the binomial theorem, which states that for any two numbers a and b, (a+b)^n = a^n + (n choose 1) * a^ (n-1) * b + (n choose 2) * a^ (n-2) * b^2 + ... + b^n.
In the case that $n=3$, the triples possible are $(i,j,k)=(3,0,0),(1,1,0),$ and $(0,0,1)$ yielding the formula: $$a^3+b^3+c^3 = s_1^3 - 3s_2s_1 + 3s_3$$ which is the result you got.
Question. If a+b+c=0. Then find the value of a 3 +b 3 +c 3. Solution. We know from the identity, a 3 +b 3 + c 3 = (a+ b + c) (a 2 + b 2 + c 2 – ab – be – ca) + 3abc. i.e. a 3 +b 3 + c 3 – 3 abc = (a + b + c) (a 2 +b 2 +c 2 –ab–bc-ca) [∴ a + b + c = 0] a 3 +b 3 + c 3 – 3abc = 0. So. a³+b³+c³=3abc. Suggest Corrections. 214. Similar questions. Q.
The formula for the cubes’ difference is a3 – b3 = (a – b) (a2 + ab + b2). The shorter diagonals on a cube’s square faces and the longer diagonals that go through its centre are of different lengths.
