good one!

JEE Mains Answers › Olympiad Stuff questions › good one!

Find all positive integral solutions (a,b,c) to the equation (a+1)(b+1)(c+1)=2(abc + 1)

#Mathematics #Olympiad Stuff

UP 0 DOWN 0 0 3
Post on FacebookPost anonymously?

3 Answers

Mani Pal Singh ·2009-04-25 05:29:30

this is a good 1
i am not having the exact idea

please disclose the solution[1]

UP 0 DOWN 0
Post on FacebookPost anonymously?

ith_power ·2009-04-25 06:04:37

(a+1)(b-1)(c-1)\ge 0 \\ \implies b+c+ac+bc \ge abc+a+bc+1 > abc +1. \\ So\\ (a+1)(b+1)(c+1)=abc+a+c+b+ac+cb+ab+1 >2(abc+1) \\ since\text{ } a+ab>0
So no positive integral solution.

UP 0 DOWN 0
Post on FacebookPost anonymously?

Mani Pal Singh ·2009-04-25 06:13:38

[339][339][339][339]

mast work
good solution

vivek please verify it

UP 0 DOWN 0
Post on FacebookPost anonymously?

Your Answer

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

Close [X]

good one!

3 Answers

Your Answer

Add Image

Similar Questions