Rewrite the expressions with rational exponents as radical expressions, and then solve the equation.
-$(10+x)^{1 / 2}+(11-5 x)^{1 / 2}=-1$
A) $\varnothing$
B) $\{0\}$
C) $\left\{-1, \frac{10}{9}\right\}$
D) $\{1\}$

Question

Quizplus · Accepted Answer

The given equation $(10+x)^{1 / 2}+(11-5 x)^{1 / 2}=-1$ involves square roots, which are always non-negative for real numbers. The sum of two non-negative numbers cannot be negative, making the equation impossible to satisfy. Therefore, there are no real solutions.

Rewrite the Expressions with Rational Exponents as Radical Expressions, and Then