2010007706
Level:
A
If \( \sqrt{x^2-x-12}=x+3 \), then the number \( x \) can be equal to:
\( -3\)
\( -4\)
\( -5\)
\( -6\)
Radical equations and inequalities
2010007705
Level:
B
Find the solution of the inequality.
\[
\sqrt{-x^2+x+2}\geq 4
\]
\(x\in\emptyset\)
\(x\in [ -3;4]\)
\(x\in\mathbb{R}\)
\(x\in [ -1;2]\)
2010007704
Level:
A
Find the domain of the expression.
\[
\sqrt{-x^2-7x+30}
\]
\([ -10;3] \)
\(\left(-\infty;-10 ] \cup[ 3;\infty\right)\)
\([ -3;10] \)
\(\emptyset\)
2010007703
Level:
A
Find the domain of the expression.
\[
\frac1{\sqrt{2x^2-11x+14}}
\]
\(\left(-\infty;2\right)\cup\left(\frac72;\infty\right)\)
\(\left(2;\frac72\right)\)
\(\left(-\infty;2\right] \cup \left[ \frac72;\infty\right)\)
\(\left[ 2;\frac72 \right] \)
2010007702
Level:
A
Find the solution of the equation.
\[
\sqrt{x^2-3x+6}=\sqrt{x^2-4x+6}
\]
\(x\in\{0\}\)
\(x\in\emptyset\)
\(x\in\mathbb{R}\)
\(x\in\mathbb{R}\setminus\{0\}\)
2010007701
Level:
A
Find the solution of the equation.
\[
\sqrt{-2x^2+3x-4}=2
\]
\(x\in\emptyset\)
\(x\in\mathbb{R}\)
\(x\in (-3;3)\)
\(x\in\{-3;3\}\)
2000004609
Level:
A
Choose the correct statement about the following equation.
\[
\sqrt{7-\sqrt{x-3}}=2
\]
The equation has just one root and the root is an even number.
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 two roots.
2000004608
Level:
A
Choose the correct statement about the following equation.
\[
\sqrt{x+5} + \sqrt{2-x}=0
\]
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.
2000004607
Level:
A
Choose the correct statement about the following equation.
\[ x-2 \sqrt{x-6} =6 \]
The roots of the equation are \(x_1=10\) and \(x_2= 6\).
The only root of the equation is \(x=6\).
The equation has no root in \( \mathbb{R}\).
The roots of the equation are \(x_1=-2\) and \(x_2=6\).
2000004606
Level:
A
Choose the correct statement about the following equation.
\[ 5+ 2\sqrt{x-2}=9\]
The solution of this equation is a number from the interval \( (5;6] \).
The solution of this equation is a number from the interval \( (-1 ; 0 ] \).
The solution of this equation is a number from the interval \( (0;3] \).
The solution of this equation is a number from the interval \( (3;5 ] \).