equation with Integer + fraction

VITEEE 2015 Online › Algebra questions › equation with Integer + fraction

\hspace{-16}$Solve The equation $\mathbf{[x]^5+\{x\}^5=x^5}$\\\\ Where $\mathbf{[x]=}$ Greatest Integer function\\\\ And $\mathbf{\{x\}=}$ Fractional part function.

#Mathematics #Algebra

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Vivek @ Born this Way ·2012-03-12 03:35:56

For x in [0,1), the equation becomes {x}⁵ = x⁵ => Which seems to be an identity true for all values in that range. Can you please confirm?

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Aditya Bhutra ·2012-03-12 06:40:01

binomially expand x⁵ = ( [x] + {x} )⁵

Solution is xâ†’ I U (0,1)

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Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

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equation with Integer + fraction

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