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KVPY2014MathematicsQuadratic Equation

Let a, b, c be non-zero real numbers such that a+b+c=0 ; let q=a²+b²+c² and r=a⁴+b⁴+c⁴ Then

Options

  1. Aq 2 < 2 r always
  2. Bq 2=2 r always
  3. Cq 2>2 r always
  4. Dq 2-2 r can take both positive and negative value

Correct answer

B. q 2=2 r always

Step-by-step solution

array l a+b+c=0, a, b, c R 0 a²+b²+c²+2(a b+b c+c a)=0 q=a²+b²+c², & r=a⁴+b⁴+c⁴ r=q²-2 (a² b²+b² c²+c² a² ) r=q²-2 [(a b+b c+c a)²-2 a b c(a+b+c) ] r=q²-2 (q² / 4 ) r=q² / 2 ANS - B array

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