How do you solve #sqrt(x^2+5)=x+3#?

1 Answer
Jul 14, 2016

Answer:

Square both sides of the equation.

Explanation:

#(sqrt(x^2 + 5))^2 = (x + 3)^2#

#x^2 + 5 = x^2 + 6x + 9#

#x^2 - x^2 - 6x + 5 - 9 = 0#

#-6x = 4#

#x = -2/3#

Checking in the original equation, we find this solution works. Hence, the solution set is #{-2/3}#.

Hopefully this helps!