9000020003
Level:
A
Find the domain of the following equation.
\[
\sqrt{3x + 6} + \sqrt{8 - 2x} = 11
\]
\([ - 2;4] \)
\((-\infty ;-2] \)
\([ - 2;\infty )\)
\([ 4;\infty )\)
Radical equations and inequalities
9000020004
Level:
A
Find the domain of the following equation.
\[
\sqrt{x - 7} + \sqrt{3x + 12} = 5
\]
\([ 7;\infty )\)
\([ - 4;7] \)
\([ - 4;\infty )\)
\((-4;7)\)
9000020005
Level:
A
Identify a true statement referring to the solution of the following equation.
\[
\sqrt{2x - 5} = 3
\]
The solution is a prime number.
The solution is an even number.
The solution is a number divisible by the number
\(3\).
The solution is an irrational number.
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
\(\mathbb{R}\).
9000020009
Level:
A
Choose the equation which is obtained by squaring both
sides of the following equation.
\[
\sqrt{3x + 2} = x - 6
\]
\(x^{2} - 15x + 34 = 0\)
\(x^{2} - 3x - 38 = 0\)
\(x^{2} - 3x - 34 = 0\)
\(x^{2} - 15x - 38 = 0\)
9000020010
Level:
A
Choose the equation which is obtained by squaring both
sides of the following equation.
\[
\sqrt{x^{2 } - x + 5} = 2x - 5
\]
\(3x^{2} - 19x + 20 = 0\)
\(x^{2} + 3x + 20 = 0\)
\(3x^{2} + x - 30 = 0\)
\(3x^{2} + x + 20 = 0\)
9000022305
Level:
A
Find the domain of the following expression.
\[
\sqrt{-x^{2 } + 16x - 63}
\]
\(\left [ 7;9\right ] \)
\(\left (-\infty ;7\right )\cup \left (9;\infty \right )\)
\(\left (-\infty ;-7\right ] \cup \left [ 9;\infty \right )\)
\(\left (7;9\right )\)
\(\left [ -7;9\right ] \)
9000022801
Level:
A
Find the domain of the expression.
\[
\sqrt{x^{2 } + x - 2}
\]
\(\left (-\infty ;-2\right ] \cup \left [ 1;\infty \right )\)
\(\left [ -2;1\right ] \)
\(\left (-2;1\right )\)
\(\left (-\infty ;-2\right )\cup \left (1;\infty \right )\)