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Most Important Selected Qs for JEE AdvancedMathematicsSequences and Series

If x₁, x₂, x₃, x₄ are four positive real numbers such that x₁+ 1 x₂ =4, x₂+ 1 x₃ =1, x₃+ 1 x₄ =4 and x₄+ 1 x₁ =1 , then

Options

  1. Ax₁=x₃
  2. Bx₂=x₄
  3. Cx₁ x₂=1
  4. Dx₃ x₄=1

Correct answer

D. x₃ x₄=1

Step-by-step solution

4=x₁+ 1 x₂ 2 x₁ x₂ 1=x₂+ 1 x₃ 2 x₂ x₃ 4=x₃+ 1 x₄ 2 x₃ x₄ 1=x₄+ 1 x₁ 2 x₄ x₁ 16= (x₁+ 1 x₂ ) (x₂+ 1 x₃ ) (x₃+ 1 x₄ ) (x₄+ 1 x₁ ) 2^4

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