Radical equations and inequalities

9000023803

Level: 
A
In the following list identify a true statement referring to the solution of the following equation. \[ \sqrt{x + 3} = 3 + x \]
The difference of the bigger and smaller solutions is \(1\).
The difference of the bigger and smaller solutions is \(- 1\).
The difference of the smaller and the bigger solutions is \(1\).
The difference of the smaller and twice the bigger solutions is \(- 1\).

9000023804

Level: 
A
Identify a true statement which concerns to the following equation. \[ \sqrt{x + 3} = x - 3 \]
The solution is in the interval \((5;8)\).
The solution is in the interval \([ - 2;2] \).
The solution is in the interval \([ - 3;1)\).
The solution is in the interval \([ 3;5)\).

9000022305

Level: 
A
Find the domain of the following expression. \[ \sqrt{-x^{2 } + 16x - 63} \]
\(\left [ 7;9\right ] \)
\(\left (-\infty ;7\right )\cup \left (9;\infty \right )\)
\(\left (-\infty ;-7\right ] \cup \left [ 9;\infty \right )\)
\(\left (7;9\right )\)
\(\left [ -7;9\right ] \)

9000023809

Level: 
A
Identify a true statement which concerns to the following equation. \[ \sqrt{16 - 5x} = 2 - x \]
The solution \(x\) satisfies \(|x| > 3\).
The solution \(x\) satisfies \(|x| < 3\).
The solution \(x\) satisfies \(|x + 1| < 3\).
The solution \(x\) satisfies \(|x + 1| > 3\).