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AP EAMCET202315 May 2023Morning ShiftMathematicsBinomial TheoremActual

If (2-5 x)^ -1 5 =a₀+a₁ x+a₂ x^2+ , then a₁ a₂ =

Options

  1. A1 3
  2. B- 2 3
  3. C- 1 3
  4. D2 3

Correct answer

D. 2 3

Step-by-step solution

aligned & (2-5 x)^ -1 / 5 =(2)^ -1 / 5 (1- 5 2 x )^ -1 / 5 & =(2)^ -1 / 5 [1+ 1 2 x+ 3 4 x^2+ ] & =(2)^ -1 / 5 + 1 2 (2)^ -1 / 5 x+ 3 4 (2)^ -1 / 5 x^2+ & Hence a₁= 1 2 (2)^ -1 / 5 and a₂= 3 4 (2)^ -1 / 5 a₁ a₂ = 2 3 aligned

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