Question

The equation $\sqrt{x+4}$- $\sqrt{x-3}$+ 1=0 has:

• A. no root
• B. one real root
• C. one real root and one imaginary root
• D. two imaginary roots
• E. two real roots

Answer 1

Answer: (A)

no root

$⟹\sqrt{x+4}-\sqrt{x-3}+1=0⟹\sqrt{x+4}+1=\sqrt{x-3}⟹x+4+1+2\sqrt{x+4}=x-3⟹2\sqrt{x+4}=-8⟹x+4=16\therefore x=12$

But x = 12 will not satisfy given equation.

$\therefore$ No roots for given equation.