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    Question

    I. (4x-5)3 +  1/(4x-5)3  =

    2 II. 2[(y+1/y)2- 2]- 9(y+1/y)= -14 In the following questions, two equations numbered I and II are given. You have to solve both the equations and find out the correct option. Give answer 
    A If x ≥y Correct Answer Incorrect Answer
    B If x ≤y Correct Answer Incorrect Answer
    C If x>y Correct Answer Incorrect Answer
    D If x Correct Answer Incorrect Answer
    E If x=y or relationship between x and y cannot be established Correct Answer Incorrect Answer

    Solution

    I. (4x-5)3+  1/(4x-5)3  = 2 Let 4x-5=a a3+  1/a3 =2  a6+ 1=2a³ a6-2a³+ 1=0  (a3- 1)2= 0  a³=1  a=1  4x-5=1  x=   3/2  II. 2[(y+1/y)2- 2]- 9(y+1/y)= -14 Put (y+1/y)=b 2[b2-2]-9b+14=0  2b2- 4-9b+14=0  2b2-9b+10=0  2b2-5b-4b+10=0  b(2b-5)-2(2b-5)=  0  b=2,5/2  If (y+1/y)= 2 y²+1=2y  y²+1-2y=0  (y-1)2= 0  y=1  If, (y+1/y)=  5/2  2y2+2=5y  2y2+2-5y=0  2y2-  4y-y+2=0 2y(y-2)-1(y-2)=0  y=2,1/2  Hence, relationship between x and y cannot be established  

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