Radical equations and inequalities

2000004605

Level: 
A
Choose the correct statement about the following equation. \[ \sqrt{4-x} = 3-\sqrt{x-4}\]
The equation has no solution in \( \mathbb{R}\).
The equation has just one root and the root is an odd number.
The equation has just one root and the root is an even number.
The equation has just two roots.

1003020602

Level: 
A
Find the domain of the expression. \[ \frac{\sqrt{x^2-x-6}}{x^2-7x+10} \]
\(\left(-\infty;-2\right]\cup\left[3;5\right)\cup\left(5;\infty\right)\)
\(\left(-\infty;-2\right)\cup\left(3;\infty\right)\)
\(\left(-\infty;-2\right)\cup\left(3;5\right)\cup\left(5;\infty\right)\)
\(\left(-\infty;2\right)\cup\left(3;5\right)\cup\left(5;\infty\right)\)

2000004602

Level: 
A
Choose the correct statement about the following equation. \[ \sqrt{5x+9} = \sqrt{x+1}\]
The equation has no solution in \( \mathbb{R} \).
The equation has just one root and the root is an odd number.
The equation has just one root and the root is an even number.
The equation has just two roots.