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NDA2018MathematicsDeterminantsActual

If a+b+c=0 , then one of the solution of | array ccc a-x & c & b c & b-x & a b & a & c-x array |=0 is

Options

  1. Ax = a
  2. Bx = 3 ( a ^2+ b ^2+ c ^2 ) 2
  3. Cx= 2 ( a ^2+ b ^2+ c ^2 ) 3
  4. Dx =0

Correct answer

D. x =0

Step-by-step solution

aligned | array ccc a-x & c & b c & b-x & a b & a & c-x array |=0 - | array ccc x-(a+b+c) & c & b x-(a+b+c) & b-x & a x-(a+b+c) & a & c-x array |=0 | array ccc x & c & b x & b-x & a x & a & c-x array |=0 Applying C ₁ C ₁+ C ₂+ C ₃ . | array ccc x & c & b 0 & c+x-b & b-a 0 & c-a & b+x-c array |=0 Applying R ₂ R ₁- R ₂ and R ₃ R ₁- R ₃ x (c+x-b)(b+x-c)-(b-a)(c-a) =0 x (x^2-(b-c)^2-b c+a c+a b-a^2 =0 . x (x^2-a^2-b^2-c^2+a b+b c+c a )=0 x x^2-(a-b)^2-(b-c)^2-(c-a)^2 =0 array ll & x=0 array aligned

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