The sum of the solutions of the equation \left | \sqrt{x}-2 \right |+\sqrt{x}\left (\sqrt{x}-4 \right )+2=0,(x>0) is equal to :

  • Option 1)

    12

  • Option 2)

    10

  • Option 3)

    9

  • Option 4)

    4

 

Answers (1)

\left | \sqrt{x}-2 \right |+\sqrt{x}\left (\sqrt{x}-4 \right )+2=0,(x>0)

\\\left | \sqrt{x}-2 \right |+x-4\sqrt{x}+2=0\\\; \; \; \\\left | \sqrt{x}-2 \right |+\left ( \sqrt{x}-2 \right )^{2}-4+2=0

\left | \sqrt{x}-2 \right |+\left ( \sqrt{x}-2 \right )^{2}-2=0

Let\; \left | \sqrt{x}-2 \right |=t

t+t^{2}-2=0

t^{2}+t-2=0

t=\frac{-1\pm \sqrt{1+3}}{2}=\frac{-1\pm 3}{2}=-2,1

\left | \sqrt{x}-2 \right |=1\; \; \; \; \; \; (as\; t>0)

\sqrt{x}-2 =\pm 1

\sqrt{x} =+1+2=3,

         =-1+2=1,

\\\sqrt{x}=3 , \; \; \; \; x=9\\\; \; \; \\\sqrt{x}=1 \; \; \; \; x=1

Sum =9+1=10

 

 

 


Option 1)

12

Option 2)

10

Option 3)

9

Option 4)

4

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