Question

Evaluate without actually calculating the cubes (using identities): (1/2)³+(1/3)³−(−5/6)³

Answer 1

we have to evaluate without actually calculating the cube (using identities) :

(1/2)³ + (1/3)³ - (-5/6)³

solution : we know from algebraic identities,

if (a + b + c) = 0 , then a³ + b³ + c³ = 3abc

here (1/2)³ + (1/3)³ - (-5/6)³

let a = 1/2 , b = 1/3 and c = -5/6

now a + b + c = 1/2 + 1/3 - 5/6 = (3 + 2 - 5)/6 = 0

hence, a + b + c = 0

so we can apply, a³ + b³ + c³ = 3abc

now (1/2)³ + (1/3)³ - (-5/6)³ = 3(1/2)(1/3)(-5/6)

= 3 × 1/2 × 1/3 × -5/6

= -5/12

Therefore the value of (1/2)³ + (1/3)³ - (-5/6)³ = -5/12