If xa × xb × xc = 1, the the value of a3 + b3 + c3 is

1.	If xa × xb × xc = 1, the the value of a3 + b3 + c3 is
Answer» Correct Answer - Option 4 : 3abc Given xa × xb × xc = 1 Formula used 1) a^m × aⁿ = a^{m + n} 2) a⁰ = 1 3) a3 + b3 + c3 − 3abc = (a + b + c)(a2 + b2 + c2 − ab − bc − ca) Calculation xa × xb × xc = 1 ⇒ x^{a + b + c} = 1 ⇒ x^{a + b + c} = x⁰ On comparing both sides we get, a + b + c = 0 a3 + b3 + c3 − 3abc = (a + b + c)(a2 + b2 + c2 − ab − bc − ca) Putting (a + b + c) = 0 we get, a3 + b3 + c3 − 3abc = 0 ⇒ a3 + b3 + c² = 3abc

Answer» Correct Answer - Option 4 : 3abc

Given

xa × xb × xc = 1

Formula used

1) a^m × aⁿ = a^{m + n}

2) a⁰ = 1

3) a3 + b3 + c3 − 3abc = (a + b + c)(a2 + b2 + c2 − ab − bc − ca)

Calculation

xa × xb × xc = 1

⇒ x^{a + b + c} = 1

⇒ x^{a + b + c} = x⁰

On comparing both sides we get,

a + b + c = 0

a3 + b3 + c3 − 3abc = (a + b + c)(a2 + b2 + c2 − ab − bc − ca)

Putting (a + b + c) = 0 we get,

a3 + b3 + c3 − 3abc = 0

⇒ a3 + b3 + c² = 3abc

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If xa × xb × xc = 1, the the value of a3 + b3 + c3 is

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