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AP EAMCET2014MathematicsBinomial Theorem

If (a+b x)⁻³= 1 27 + 1 3 x+ , then the ordered pair (a, b) equals to

Options

  1. A(3,-27)
  2. B(1, 1 3 )
  3. C(3,9)
  4. D(3,-9)

Correct answer

D. (3,-9)

Step-by-step solution

aligned Now, (a+b x)⁻³ & =a⁻³ (1+ b x a )⁻³ & = 1 a^3 (1- ^3 C₁ ( b x a )+ ) 1 a^3 & - ^3 C₁ 1 a^3 ( b x a )+ & = 1 27 + 1 3 x aligned (given) On equating constant and x , we get 1 a^3 = 1 27 array rlrl and & - ^3 C₁ 1 a^3 ( b a ) & = 1 3 & r l r l and & - ^3 C₁ ( 1 3^4 ) b & = 1 3 & -3 1 3^4 b & = 1 3 & & -b & =3^2 b=-9 & & (a, b) & =(3,-9) array

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