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KVPY2016MathematicsQuadratic Equation

Suppose a is a positive real number such that a⁵-a³+a=2 . Then

Options

  1. Aa⁶ < 2
  2. B2 < a⁶ < 3
  3. C3 < a ⁶ < 4
  4. D4 a ⁶

Correct answer

C. 3 < a ⁶ < 4

Step-by-step solution

a⁵-a³+a=2 ; a R⁺ Let f ( a )= a ⁵- a ³+ a -2 ; Note . f ( a )>0 a R for a⁶=3 a=3^ 1 / 6 =1.2 use calculator we get f (1.2) 0 so one root in a (3,4)

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