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If and are the real roots of the equation 5 x x-2 + x-2 5 x = 29 10 and > , then ^2-11^4 ^2 =

Options

  1. A64
  2. B36
  3. C100
  4. D6

Correct answer

D. 6

Step-by-step solution

We have, 5 x x-2 + x-2 5 x = 29 10 Let 5 x x-2 =y Then, y+ 1 y = 29 10 y^2+1 y = 29 10 10 y^2+10=29 y 10 y^2-29 y+10=0 10 y^2-25 y-4 y+10=0 5 y(2 y-5)-2(2 y-5)=0 (5 y-2)(2 y-5)=0 y= 2 5 , 5 2 Now, if y= 2 5 5 x x-2 = 2 5 5 x x-2 = 4 25 125 x=4 x-8 121 x=-8 x=-8 / 121 And if y= 5 2 5 x x-2 = 5 2 5 x x-2 = 25 4 x x-2 = 5 4 5 x-10=4 x x=10 Let =10 and = -8 121 ( > ) ^2-11^4 ^2 = (10)^2-11^4 ( -8 121 )^2 = 100-64 = 36 =6

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