value of :(xa/xb)a+b×(xb/xc)b+c×(xc/xa)c+a
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Answer:
(xᵃ/xᵇ)⁽ᵃ⁺ᵇ⁾ * (xᵇ/xⁿ)⁽ᵇ⁺ⁿ⁾ * (xⁿ/xᵃ)⁽ⁿ⁺ᵃ⁾ = 1
Step-by-step explanation:
value of :(xa/xb)a+b×(xb/xc)b+c×(xc/xa)c+a
Replacing c with n for easy typing
(xᵃ/xᵇ)⁽ᵃ⁺ᵇ⁾ * (xᵇ/xⁿ)⁽ᵇ⁺ⁿ⁾ * (xⁿ/xᵃ)⁽ⁿ⁺ᵃ⁾
= (x⁽ᵃ⁻ᵇ⁾)⁽ᵃ⁺ᵇ⁾ * (x⁽ᵇ⁻ⁿ⁾)⁽ᵇ⁺ⁿ⁾ * (x⁽ⁿ-ᵃ⁾)⁽ⁿ⁺ᵃ⁾
= x⁽ᵃ²⁻ᵇ²⁾ * x⁽ᵇ²⁻ⁿ²⁾ * x⁽ⁿ²⁻ᵃ²⁾
= x⁽ᵃ²⁻ᵇ² ⁺ ᵇ²⁻ⁿ² + ⁿ²⁻ᵃ²⁾
= x⁰
= 1
(xᵃ/xᵇ)⁽ᵃ⁺ᵇ⁾ * (xᵇ/xⁿ)⁽ᵇ⁺ⁿ⁾ * (xⁿ/xᵃ)⁽ⁿ⁺ᵃ⁾ = 1
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