1.

The equation `sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sqrt(x-1))=` hsA. No solutionB. Exactly two distinct solutionsC. Exactly four distinct solutionsD. Infinitely may solutions

Answer» Correct Answer - D
`sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sqrt(x-1))=1,Xge1`
`sqrt((x+1)-2xx2sqrt(x-1)+4)+sqrt((x-1)-6sqrt(x-1)+9)=1`
`|sqrt(x-1)-2|+|sqrt(x-1)-3|=1`
Case - 1
`sqrt(x-1)-2+sqrt(x-1)-3=1" "xge10`
`2sqrt(x-1)=6`
x = 10
Case - II
`sqrt(x-1)-2-sqrt(x-1)+3=1" "5lexle10`
Case - III
`-sqrt(x-1)+2-sqrt(x-1)+3=1" "1lexle5`
`2sqrt(x-1)=4`
x = 5


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