1003019901
Level:
A
Find the solution of the equation.
\[
\sqrt{-3x^2+2x+5}=3
\]
\(x\in\emptyset\)
\(x\in[-2;2]\)
\(x\in\{-2;2\}\)
\(x\in\mathbb{R}\)
Radical equations and inequalities
9000034903
Level:
A
Find all \(x\in \mathbb{R}\)
for which the following expression is undefined.
\[
\sqrt{\left (3x + 4 \right ) \left (\frac{1}
{5} - x\right )}
\]
\(\left (-\infty ;-\frac{4}
{3}\right )\cup \left (\frac{1}
{5};\infty \right )\)
\(\left [ -\frac{4}
{3}; \frac{1}
{5}\right ] \)
\(\left (-\infty ;-\frac{4}
{3}\right ] \cup \left [ \frac{1}
{5};\infty \right )\)
\(\left (-\frac{4}
{3}; \frac{1}
{5}\right )\)
9000034901
Level:
A
Find the domain of the following expression.
\[
\sqrt{\left (2x - 3 \right ) \left (3x + 1 \right )}
\]
\(\left (-\infty ;-\frac{1}
{3}\right ] \cup \left [ \frac{3}
{2};\infty \right )\)
\(\left [ -\frac{1}
{3}; \frac{3}
{2}\right ] \)
\(\left (-\frac{1}
{3}; \frac{3}
{2}\right )\)
\(\left (-\infty ;-\frac{1}
{3}\right )\cup \left (\frac{3}
{2};\infty \right )\)
9000033702
Level:
A
Find the domain of the following expression.
\[
\sqrt{-x^{2 } + 7x - 12} -\frac{1}
{x}
\]
\([ 3;4] \)
\(\mathbb{R}\setminus \left \{0\right \}\)
\(\mathbb{R}\setminus \left \{0;3;4\right \}\)
\(\left (3;4\right )\)
\(\left (-\infty ;3\right )\cup \left (4;\infty \right )\)
\(\left (-\infty ;3] \cup [ 4;\infty \right )\)
9000024801
Level:
B
In the following list identify an inequality which does not have a solution.
\(\sqrt{2x - 3} < -6\)
\(\sqrt{x^{2 } - 3x} > 5\)
\(\sqrt{1 + x^{2}} > -10\)
\(\sqrt{2x^{2}} < 4\)
9000024804
Level:
B
How many solutions does the inequality
\[
\sqrt{x + 17} > x - 3
\]
have in the set \(\mathbb{N}\)?
Seven solutions in \(\mathbb{N}\).
No solution in \(\mathbb{N}\).
Five solutions in \(\mathbb{N}\).
More than seven solutions in \(\mathbb{N}\).
9000024805
Level:
C
A falling body dropped at a velocity
\(60\, \mathrm{m}\mathrm{s}^{-1}\). Find the
initial height \(h\),
if the relation between the velocity and the initial height
\(h\) is
\(v = \sqrt{2hg}\). Use
\(g = 10\, \mathrm{m}\mathrm{s}^{-2}\) for
acceleration of gravity.
The initial height is between \(150\, \mathrm{m}\)
and \(200\, \mathrm{m}\).
The initial height is smaller than \(100\, \mathrm{m}\).
The initial height is between \(100\, \mathrm{m}\)
and \(150\, \mathrm{m}\).
The initial height is bigger than \(200\, \mathrm{m}\).
9000024809
Level:
B
Find the solution set of the following inequality.
\[
\sqrt{x + 3} > x - 3
\]
\([ -3;6)\)
\( (1;6)\)
\([ -3;3] \)
\( (-\infty ;1)\cup (6;+\infty )\)
9000024810
Level:
C
Find the solution set of the following inequality.
\[
\sqrt{|x|} > x
\]
\(K = (-\infty ;0)\cup (0;1)\)
\(K = (-\infty ;1)\)
\(K =\mathbb{R} ^{+}\)
\(K = (0;1)\)
9000024802
Level:
A
Consider the equation
\[
\sqrt{x^{2 } - 2x + 1} = x + 2
\]
and the equation which arises from this equation by squaring both sides of the
equation, i.e. the equation
\[
\left (\sqrt{x^{2 } - 2x + 1}\right )^{2} = (x + 2)^{2}.
\]
Identify a true statement.
Both equations are equivalent only if
\(x\geq - 2\).
Both equations are equivalent.
Both equations are equivalent only if
\(x\leq - 2\).
None of the above.