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AP EAMCET2009MathematicsBinomial Theorem

1 e^ 3 x (e^x+e^ 5 x )=a₀+a₁ x+a₂ x^2+ 2 a₁+2^3 a₃+2^5 a₅+ is equal to

Options

  1. Ae
  2. Be⁻¹
  3. C1
  4. D0

Correct answer

D. 0

Step-by-step solution

aligned & Given, 1 e^ 3 x (e^x+e^ 5 x )=a₀+a₁ x+a₂ x^2+ & (e^ -2 x +e^ 2 x )=a₀+a₁ x+a₂ x^2+ & 2 [1+ (2 x)^2 2 ! + (2 x)^4 4 ! + ] & =a₀+a₁ x+a₂ x^2+ & a₁=a₃=a₅= =0 & 2 a₁+2^3 a₃+2^5 a₅+ =0 & aligned

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