Homework Help

If `sqrt (x+3) + sqrt (x-2) = 5` , then the value of x is  ____ ?This is a question I...

user profile pic

nasirjam | Student, Grade 9 | (Level 2) Honors

Posted October 10, 2012 at 11:09 AM via web

dislike 2 like

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...

1 Answer | Add Yours

user profile pic

mjripalda | High School Teacher | (Level 1) Senior Educator

Posted October 10, 2012 at 11:35 AM (Answer #1)

dislike 1 like

`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.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes