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Solve sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sq...

Solve `sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sqrt(x-1))=1`

Text Solution

Verified by Experts

`sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sqrt(x-1))=1`
`or sqrt(x-1-4sqrt(x-1)+4)+sqrt(x-1-6sqrt(x-1))=1`
`or sqrt(|sqrt(x-1)-2|^2)+ sqrt(|sqrt(x-1)-3|^2)=1`
or `|sqrt(x-1)-2|+|sqrt(x-1)-3|=1`
or `|sqrt(x-1)-2|+|sqrt(x-1)-3|=(sqrt(x-1)-2)-(sqrt(x-1)-3)`
`rArr sqrt(x-1)-2 ge 0 and sqrt(x-1)-3 le 0 `
`rArr 4 le x-1 le9`
`rArr 5 lex le 10`
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