Solve `sqrt(x+65) + sqrt(5-x) = 4`

Explanation

Squaring the term of the both the sides, we get
`(sqrt(x+5) +sqrt(5-x))^(2) = 4^(2)`
`rArr x + 5 + 5 - x + 2 sqrt((x+5)(5-x)) = 16`
`rArr 10 +2 sqrt(25-x^(2)) = 16`
`rArr sqrt(25-x^(2)) = 3`
Squaring the term on the both the sides again, we get
`25 - x^(2) = 3^(2)`
`rArr x^(2) = 25 - 9`
`rArr x^(2) = 16 rArr x = +- 14`
`:. - 4` and 4 are the required solution of the given equation.