Let x = a(b − c), y = b(c − a) and z = c(a − b), with abc ≠ 0. Then (x/a)³ + (y/b)³ + (z/c)³ equals

Question

Accepted Answer

3xyz/(abc). x/a + y/b + z/c = (b − c) + (c − a) + (a − b) = 0. When three numbers add up to 0, the sum of their cubes is 3 × their product: 3·(x/a)(y/b)(z/c) = 3xyz/(abc).

Let $x = a (b - c), y = b (c - a)$ and $z = c (a - b)$ , with $ab c$ ≠ 0. Then $(x / a)^{3} + (y / b)^{3} + (z / c)^{3}$ equals

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Algebra practice

Let x=a(b−c),y=b(c−a) and z=c(a−b), with abc ≠ 0. Then (x/a)3+(y/b)3+(z/c)3 equals

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Algebra practice

Let $x = a (b - c), y = b (c - a)$ and $z = c (a - b)$ , with $ab c$ ≠ 0. Then $(x / a)^{3} + (y / b)^{3} + (z / c)^{3}$ equals