The sum of the solutions of the equation
`|sqrtx-2|+sqrtx(sqrtx-4)+2=(x gt0)` is equal to
A. 9
B. 12
C. 4
D. 10
`|sqrtx-2|+sqrtx(sqrtx-4)+2=(x gt0)` is equal to
A. 9
B. 12
C. 4
D. 10
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Correct Answer – 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`