Decide what values of the variable cannot possibly be solutions for the equation.
-$$( 3 x + 1 ) ^ { 1 / 2 } = 3 + ( x - 4 ) ^ { 1 / 2 }$$
A) $\{ 5,8 \}$
B) $\varnothing$
C) $\{ - 1 \}$
D) $\{ - 5 , - 8 \}$

Question

Quizplus · Accepted Answer

The equation involves square roots, which are only defined for non-negative numbers. Therefore, $3x + 1 \geq 0$ and $x - 4 \geq 0$. Solving these inequalities, we get $x \geq -\frac{1}{3}$ and $x \geq 4$. Thus, $x$ must be at least 4. Testing the values in the set $\{5, 8\}$, we find they do not satisfy the equation, making them impossible solutions.

Decide What Values of the Variable Cannot Possibly Be Solutions (3x+1)1/2=3+(x−4)1/2( 3 x + 1 ) ^ { 1 / 2 } = 3 + ( x - 4 ) ^ { 1 / 2 }(3x+1)1/2=3+(x−4)1/2

Decide What Values of the Variable Cannot Possibly Be Solutions $( 3 x + 1 ) ^ { 1 / 2 } = 3 + ( x - 4 ) ^ { 1 / 2 }$