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Number of real solution of 5- ₂|x| =3- ₂|x| is equal to

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

B. 2

Step-by-step solution

aligned & Let & ₂|x| & =t (i) & & 5-t & =3-t & & 5-t & =(3-t)^2 & & 5-t & =9+t^2-6 t aligned aligned & t^2-5 t+4=0 & (t-4)(t-1)=0 & t=1 or 4 [rejected] & [ 5-4 =3-4,1 -1] & ₂|x|=1 & |x|=2 & x= 2 aligned Total 2 real solutions.

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