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Find all the solutions of the equation , [(2|x| – 3) 2 - |x| – 6]/(4x+1 ) =0 which belong to the domain of definition of the function y= (2x+1) /(x – 36) the answer is given as x = +3 and – 3 but i think it x= +1/4 is also a solution.

Find all the solutions of the equation  , [(2|x| – 3)2-   |x| –  6]/(4x+1 ) =0 which belong to the domain of definition of the function y= (2x+1) /(x – 36)  the answer is given as x = +3 and – 3 but i think it x= +1/4 is also a solution.

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1 Answers

Vikas TU
14149 Points
7 years ago
Solving numerator,
(2|x| – 3)2-   |x| –  6 = > 4|x|^2 + 9 – 12|x| – |x| – 6  =>  4|x|^2 -13|x| + 3 = 0
= > 4|x|^2 -12|x| – |x|  + 3 = 0
= > 4|x|(|x| – 3) – (|x| – 3) = 0
=> (4|x| – 1) (|x| – 3) = 0
|x| = 3
x = + 3 and x = – 3
x = + ¼  and x = -1/4
Now the domain of the function y= (2x+1) /(x – 36) is:  R – {36}
so possible solutions are all values of x except 36.

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