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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.
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| = 3x = + 3 and x = – 3x = + ¼ and x = -1/4Now 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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