#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# Find x^1/3 + y^1/3 + z^1/3 = 0Then find (x + y + z)^3

Arun Kumar IIT Delhi
6 years ago
Hello Student

$\\Let x^{1/3} = a, y^{1/3} = b, z^{1/3} = c \\The question then becomes, if (a+b+c) = 0 \\ then what is the value of (a^3+b^3+c^3)^3. \\We have a+b = -c. \\=> (a+b)^3 = (-c)^3 = -c^3. \\=> a^3+b^3+3*a*(b^2)+3*(a^2)*b = -c^3 \\=> a^3+b^3+c^3 = -{ 3*a*(b^2)+3*(a^2)*b } = -3*a*b*(a+b) = -3*a*b*(-c) = 3abc. \\=> (a^3+b^3+c^3)^3 = (3abc)^3 = 27(a^3)(b^3)(c^3) = 27xyz.$

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Pallavi Das
17 Points
6 years ago
we know if a+b+c=0 then a^3+b^3+c^3=3abc
so ifx^1/3 + y^1/3 + z^1/3 = 0 then
x+y+z=3.x^1/3.y^1/3.z^1/3
so (x+y+z)^3=(3.x^1/3.y^1/3.z^1/3)^3
(x+y+z)^3=27xyz

Rishi Sharma
10 months ago
Dear Student,

we know if a + b + c = 0 then
a^3 + b^3 + c^3 = 3abc
so if x^1/3 + y^1/3 + z^1/3 = 0 then
x + y + z = 3.x^1/3.y^1/3.z^1/3
so ( x + y + z )^3 = (3.x^1/3.y^1/3.z^1/3)^3
(x+y+z)^3 = 27xyz

Thanks and Regards