smc

Simplify. $$\sqrt{x+4}=\sqrt{x-3}-1$$ $$x+4=x-3-2\sqrt{x-3}+1$$ $$6=-2\sqrt{x-3}$$ We don't need to solve any further. The square root term is negative, therefore there will be no real roots. The answer is $\boxed{\text{no root}}.$