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Soln-
a¹/³ + b ¹/³ + c ¹/³ = 0
=» (a¹/³)³ + (b ¹/³)³ + (c ¹/³)³
. . . .=3(a¹/³)(b¹/³)(c¹/³)
=» a + b + c = 3a¹/³b¹/³c¹/³
a¹/³ + b ¹/³ + c ¹/³ = 0
=» (a¹/³)³ + (b ¹/³)³ + (c ¹/³)³
. . . .=3(a¹/³)(b¹/³)(c¹/³)
=» a + b + c = 3a¹/³b¹/³c¹/³
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⭐Solution⭐
✏given here
³√a + ³√b + ³√c = 0......(1)
✏Find here
(a+b+c)³ = ❓
We know ,
(x+y+x)³= (x³+y³+z³)+3(x+y)(y+z)(z+x)
So,
by (1),
(³√a + ³√b +³√c)³
= (³√a)³ + (³√b)³ + (³√c)³ + 3(³√a + ³√b)(³√b + ³√c)(³√c + ³√a)
= (a+b+c) + 3(³√a + ³√b)(³√b + ³√c)(³√c + ³√a)........(2)
keep value by (1)
(0) = (a+b+c) + 3(³√a + ³√b)(³√b + ³√c)(³√c + ³√a)
=> (a+b+c) + 3(³√a + ³√b)(³√b + ³√c)(³√c + ³√a) = 0
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✏Hopes it's right and helps u.
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