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AP EAMCET2012MathematicsQuadratic Equation

The product of real of the equation |x|^ 6 / 5 -26|x|^ 3 / 5 -27=0

Options

  1. A-3¹⁰
  2. B-3¹²
  3. C-3^ 12 / 5
  4. D-3^ 21 / 5

Correct answer

A. -3¹⁰

Step-by-step solution

Given equation is |x|^ 6 / 5 -26|x|^ 3 / 5 -27=0 Put |x|^ 3 / 5 =t aligned & t^2-26 t-27=0 & t^2-27 t+t-27=0 & t(t-27)+1(t-27)=0 & (t+1)(t-27)=0 & t=27 or -1 & |x|^ 3 / 5 =27 & ( |x|^ 3 / 5 can not be negative) . & |x|^3= (3^3 )^5 & |x|=3^5 & x=3^5 or -3^5 & aligned Product of x=3^5 (-3)^5=-3¹⁰

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