A

9000020006

Level: 
A
Identify a true statement referring to the solution of the following equation. \[ \sqrt{3x - 8} = x - 6 \]
The equation has a unique solution and this solution is an odd number.
The equation has two solutions, the sum of these solutions is divisible by \(5\).
The equation has a unique solution and this solution is an even number.
The equation does not have a solution in \(\mathbb{R}\).

9000020007

Level: 
A
Identify a true statement referring to the solution of the following equation. \[ \sqrt{x^{2 } - 4} = x + 1 \]
The equation does not have a solution in \(\mathbb{R}\).
The equation has a unique negative solution.
The equation has a unique positive solution.
The equation has two solutions.

9000020008

Level: 
A
Identify a true statement referring to the solution of the following equation. \[ 6x - 13\sqrt{x} + 6 = 0 \] Hint: Use the substitution \(y = \sqrt{x}\).
The solutions \(x_{1}\) and \(x_{2}\) satisfy \(x_{1} = \frac{1} {x_{2}} \).
The equation has a unique solution \(x_{1}\). This solution satisfies \(x_{1} < 1\).
The equation has a unique solution \(x_{1}\). This solution satisfies \(x_{1} > 1\).
The equation does not have a solution in \(\mathbb{R}\).

9000019807

Level: 
A
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation. \[ \left (3x + 2\right )\left (x\sqrt{2} + 1\right )\left (x^{2} + 1\right ) = 0 \]
\(\left \{-\frac{\sqrt{2}} {2} ;-\frac{2} {3}\right \}\)
\(\left \{-\frac{2} {3}; \frac{1} {\sqrt{2}}\right \}\)
\(\left \{\frac{2} {3}; \frac{1} {\sqrt{2}}\right \}\)
\(\left \{-1;-\frac{\sqrt{2}} {2} ;-\frac{2} {3}\right \}\)