If `sqrt (x+3) + sqrt (x-2) = 5` , then the value of x is  ____ ?This is a question I got while preparing for NTSE, PLZ sove it ASAP...

Expert Answers
lemjay eNotes educator| Certified Educator

`sqrt(x+3) + sqrt(x-2) = 5`

To remove the radicals, perform the opposite operation of square root. So, take the square of both sides.

`(sqrt(x+3) + sqrt(x-2))^2 = 5^2`

`x+3 + 2sqrt(x+3)*sqrt(x-2) + x-2=25`


Then, isolate the radical term.



Take the square of both sides again to eliminate the radicals.





Note that the terms `4x^2` appears on both sides of the equation. So if we move the `4x^2` from the right to left, the resulting expression is:


Then, bring together the terms with x on one side of the equation. Also, bring together the terms without x on the opposite side of the equation.



Then, isolate x.



Hence, the value of x is 6.