Question

If a^1/3+b^1/3 +c^1/3 ) = 0, then the value of (a+b+c)^3 will be:
1) 9a'b?c?
2) 3abc
3) 6abc
4) 27abc​

Answer 1

Answer:

Since

a1/3 +b1/3 +c1/3 =0

(a1/3)3 +(b1/3)3 +(c1/3)3

=3a 1/3

b 1/3

c 1/3

⇒a+b+c=3(abc)1/3

⇒(a+b+c)3

=27abc

Answer 2

Answer

4) 27abc

Given:

• a^⅓ + b^⅓ + c^⅓ = 0

To find:

• The value of (a + b + c)³

Solution:

a^⅓ + b^⅓ + c^⅓ = 0...given

=> a⅓ = - b^⅓ - ⅓ ...(1)

On taking cube of both sides

=> a = - b - c - 3b^⅓ c^⅓ (b^⅓ + c^⅓)]...(2)

...Indentity used (a + b)³ = a³ + b³ + 3ab (a + b)

Now,

=> (a + b + c)³

Substitute equation (2) we get,

=> { [ -b - c - 3b^⅓ c^⅓ (b^⅓ + c^⅓) + b + c ] }³

=> [ -3 b^⅓ c^⅓ (b^⅓ + c^⅓) ]³

=> - 27bc (b^⅓ + c^⅓)³

=> - 27bc [- ( - b^⅓ - c^⅓) ]³

Substitute equation (1) we get

=> - 27bc [ - (a⅓) ]³

=> 27abc

Hence, the value of (a + b + c)³ is 27abc.