Question

If x⅓ + y⅓ + z⅓ = 0 than find the value of x+y+z​

Answer 1

Given,

x⅓ + y⅓ + z⅓ = 0....(1)

We know,

If a + b + c = 0.... (2)

Then,

a^3 + b^3 + c^3 = 3*a*b*c....(3)

From (1), (2) and (3)

Assuming a = x⅓

b = y⅓

c = z⅓

Solving,

(x⅓)^3 + (y⅓)^3 + (z⅓)^3 = 3*x⅓*y⅓*z⅓

x + y + z = 3(xyz)⅓

Hence,

The required answer is 3(xyz)⅓

In these types of questions, the use of identities like a^3 + b^3 + c^3 = 3abc should be crystal clear to the students as in exams the questioner will indirectly ask the first step of the identity and you'll have to figure out the answer from the second ✔

Answer 2

Given,

x⅓ + y⅓ + z⅓ = 0....(1)

We know,

If a + b + c = 0.... (2)

Then,

a^3 + b^3 + c^3 = 3*a*b*c....(3)

From (1), (2) and (3)

Assuming a = x⅓

b = y⅓

c = z⅓

Solving,

(x⅓)^3 + (y⅓)^3 + (z⅓)^3 = 3*x⅓*y⅓*z⅓

x + y + z = 3(xyz)⅓

Hence,

The required answer is 3(xyz)⅓

In these types of questions, the use of identities like a^3 + b^3 + c^3 = 3abc should be crystal clear to the students as in exams the questioner will indirectly ask the first step of the identity and you'll have to figure out the answer from the second ✔