What is the solution set of the equation?

Question

√5-x +3=x

 

 

+3 is not under the radical

Answer 1

√(5-x) + 3 = x

 

Isolate the radical:  √(5-x) = x-3

 

Square both sides:  5-x = x² - 6x + 9

 

Solve for x:  x² - 5x + 4 = 0

 

                  (x-4)(x-1) = 0

 

                   x = 4 or 1

 

Note that 1 does not satisfy the original equation, so 1 must be excluded from the solution set.

 

So, the only solution is 4.  

 

 

Answer 2

√(5-x) = x -3

5-x = (x-3)² = x² -6x + 9

0 = x² - 5x + 4

0 = (x-1)(x-4)

 

{1,4}