Solve `sqrt(x+5)sqrt(x+21)=sqrt(6x+40.)`

Answer

`x = 4`

Explanation

`sqrt(x + 5) + sqrt( x + 21) = sqrt( 6x + 40)`.
or `(sqrt(x + 5) + sqrt( x + 21))^(2) = 6x + 40`.
`(x + 5)+(x + 21)+ 2sqrt((x + 5)( x + 21)) = 6x + 40`.
or `sqrt((x + 5)( x + 21))= 2x + 7`
or `(x + 5) (x + 21) = (2x + 7)^(2)`
or `3x^(2) + 2x - 56 = 0`
or `(3x + 14) (x - 4) = 0`
`rArr x = 4, - 14//3`
Cearly.` x = - 14//3` dos not satisfy the original equation. Hence, x = 4 is the only root of the given equation.