Question

if a^1/3+b^1/3+c^1/3 then value of (a+b+c)^3

Answer 1

Let  p=a13⟹p3=ap=a13⟹p3=a

q=b13⟹q3=bq=b13⟹q3=b

r=c13⟹r3=cr=c13⟹r3=c

Given:  a13+b13+c13=0a13+b13+c13=0

⟹p+q+r=0⟹p+q+r=0

⟹p3+q3+r3=3pqr⟹p3+q3+r3=3pqr

⟹a+b+c=3pqr⟹a+b+c=3pqr

⟹(a+b+c)3=(3pqr)3=27p3q3r3=27abc⟹(a+b+c)3=(3pqr)3=27p3q3r3=27abc

Ans: 27abc