Question

without actual method find cubes of (1/2)^3+(1/3)^3-(5/6)^3

Answer 1

by identity
$(a)^{3} +(b )^{3} +(c)^{3} = (a + b + c)((a)^{2} + (b)^{2} + (c)^{2} ) - 3abc$
(1/2+1/3-5/6)(1/2^2+1/3^3+-5/6^2) -3×1/2×1/3×-5/6
(0)(")+5/18
5/18
the answer is 5/12