1. equality

1.Transform the expression disappearing the root from the consequent.
1/(5)1/3-(2)1/3 (1/3 is the exponent)

2.Prove that for evry real x, y and z it's true:
(x-y)3+(y-z)3+(z-x)3=3*(x-y)*(y-z)*(z-x)

2. Originally Posted by blertta
1.Transform the expression disappearing the root from the consequent.
1/(5)1/3-(2)1/3 (1/3 is the exponent)

2.Prove that for evry real x, y and z it's true:
(x-y)3+(y-z)3+(z-x)3=3*(x-y)*(y-z)*(z-x)
2. Put x - y = m, y - z = n then z - x = -(m+n)
LHS = m^3 + n^3 - (m+n)^3 = -3 (mn^2 + nm^2) = -3mn(m+n)
RHS = 3mn * -(m+n) = LHS.

I don't understand Q 1.

3. For the first problem, multiply top and bottom by $5^{2/3} + 5^{1/3}2^{1/3} + 2^{2/3}$.

For the second problem, it's just a matter of multiplying out both sides of the expression. Use binomial expansion on the left side.