A Pick from Mathlinks

IIT JEE Sample Questions › Olympiad Stuff questions › A Pick from Mathlinks

Solve for positive reals (x,y,z)

z^2+2xyz=1
3x^2y^2+3y^2x=1+x^3y^4
z+zy^4+4y^3=4y+6y^2z

It's been a while no -one has really given any elaborate soln for this.....

#Mathematics #Olympiad Stuff

UP 0 DOWN 0 0 2
Post on FacebookPost anonymously?

2 Answers

Devil ·2009-12-20 08:26:06

The reason I posted it here was that some guy in mathlinks used an useful substtituiton of putting x as tanÎ¸...but my query is why such a substitution - I mean what hinted at that?

UP 0 DOWN 0
Post on FacebookPost anonymously?

Lokesh Verma ·2009-12-21 08:05:30

The hint of such a substitution comes from equation 2...

which is also a quadratic in y²

Think of the formula of tan 3k... specially in the second equation..

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]

A Pick from Mathlinks

2 Answers

Your Answer

Add Image

Similar Questions