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The sum of the solutions of the equation...

The sum of the solutions of the equation
`|sqrtx-2|+sqrtx(sqrtx-4)+2= 0,(x gt0)` is equal to

A

9

B

12

C

4

D

10

Text Solution

Verified by Experts

The correct Answer is:
D
Key Idea Reduce the given equation into quadratic equation.
Given equation is
`|sqrtx-2|+sqrtx(sqrtx-4)+2=0 implies|sqrtx-2|+x-4sqrt+4=2`
`implies|sqrtx-2|+(sqrtx-2)^(\2)=2`
`implies(|sqrtx-2|)^(2)+|sqrtx-2|-2=0`
Let `|sqrtx-2|=y,` then above equation reduced to `y^(2)+y-2=0impliesy^(2)+2y-y-2=0`
`impliesy(y+2)-1(y+2)=0implies(y+2)(y-1)=0`
`impliesy=1,-2`
`impliesthereforey=1" "[becausey="sqrtx-2|ge0]`
`implies|sqrtx-2"=1`
`impliessqrtx=pm1`
`impliessqrtx=3or 1`
`impliesx=9or1`
`therefore" Sum of roots"=9+1=10`
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