2010007702
Level:
A
Find the solution of the equation.
\[
\sqrt{x^2-3x+6}=\sqrt{x^2-4x+6}
\]
\(x\in\{0\}\)
\(x\in\emptyset\)
\(x\in\mathbb{R}\)
\(x\in\mathbb{R}\setminus\{0\}\)
Radical equations and inequalities
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 \( (3;5 ] \).
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.
2000004604
Level:
A
Choose the correct statement about the following equation.
\[ 4+ 2\sqrt{x+4} =x\]
The root of the equation is \(x=12\).
The equation has no root in \( \mathbb{R}\).
The roots of the equation are \(x_1=0\) and \(x_2=12\).
The roots of the equation are \(x_1=4\) and \(x_2= -2\).
2000004603
Level:
A
Choose the correct statement about the following equation.
\[ 2\sqrt{x-5} =2\]
The equation has just one positive root.
The equation has just one negative root.
The equation has two roots.
The equation has no solution in \( \mathbb{R}\).
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.