Question:৮.সমাধান কর:
(iv). `(sqrt(x-1) + sqrt(x-6))/(sqrt(x-1) - sqrt(x-6)) = 5` 

Answer ৮.(iv).সমাধান:
`(sqrt(x-1) + sqrt(x-6))/(sqrt(x-1) - sqrt(x-6)) = 5`

   বা, `(sqrt(x-1) + sqrt(x-6) + sqrt(x-1) - sqrt(x-6))/(sqrt(x-1) + sqrt(x-6) - sqrt(x-1) + sqrt(x-6)) = (5 + 1)/(5 - 1)`   [ যোজন-বিয়োজন করে ]

   বা, `(2sqrt(x-1))/(2sqrt(x-6)) = 6/4`

   বা, `(sqrt(x-1))/(sqrt(x-6)) = 3/2`

   বা, `((sqrt(x-1))/(sqrt(x-6)))^2 = (3/2)^2`   [ উভয়পক্ষকে বর্গ করে ]

   বা, `((sqrt(x-1))^2)/((sqrt(x-6))^2) = 9/4`

   বা, `(x - 1)/(x - 6) = 9/4`

   বা, `9(x - 6) = 4(x - 1)`   [ আড়গুণন করে ]

   বা, `9x - 54 = 4x - 4`

   বা, `9x - 4x = - 4 + 54`

   বা, `5x = 50`

   বা, `x = (50)/5`

   `:. x = 10`

`:.` নির্ণেয় সমাধান, `x = 10` 

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