Question

(i) lf a + b + c = 0 then a³ + b³ + c³ = 0

(ii) If `x - 1/x = 3` then `x^3 - 1/x^3 = 36`

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (ii)

Explanation:

(i) If a + b + c = 0, then the identity is a³ + b³ + c³ = 3abc not zero. 

So the statement (i) If a + b + c = 0 then a³ + b³ + c³ = 0 is false.

(ii) If `x - 1/x = 3`, then using the identity for cubes:

`x^3 - 1/x^3 = (x - 1/x)^3 + 3(x - 1/x)`

Calculating this gives:

`x^3 - 1/x^3 = 3^3 + 3 xx 3`

`x^3 - 1/x^3 = 27 + 9`

`x^3 - 1/x^3 = 36`

Therefore, statement (ii) is true.

Hence, only (ii) is correct.