1003019902
Level:
A
Find the solution of the equation.
\[
\sqrt{x^2-4x+3}=\sqrt{x^2-6x+3}
\]
\(x\in\{0\}\)
\(x\in\mathbb{R}\)
\(x\in\emptyset\)
\(x\in\mathbb{R}\setminus\{0\}\)
A
1003019901
Level:
A
Find the solution of the equation.
\[
\sqrt{-3x^2+2x+5}=3
\]
\(x\in\emptyset\)
\(x\in[-2;2]\)
\(x\in\{-2;2\}\)
\(x\in\mathbb{R}\)
1003020001
Level:
A
Find the sum of the roots of the equation.
\[
4x^2+2x=0
\]
\(-\frac12\)
\(0\)
\(2\)
\(-2\)
1003019801
Level:
A
Find the domain of the expression.
\[
\frac{x^2+4x-5}{-3x^2-19x+14}
\]
\(\mathbb{R}\setminus\left\{-7;\frac23\right\}\)
\(\mathbb{R}\setminus\left\{7;-\frac23\right\}\)
\(\left(7;-\frac23\right)\)
\(\left(-7;\frac23\right)\)
9000375401
Level:
A
Find a set of the values of the real parameter
\(a\) which
ensure that the following equation has a unique solution.
\[
a^{3}x + 4a - 1 = a^{2}x + 3
\]
\(\mathbb{R}\setminus \{0;1\}\)
\(\mathbb{R}\setminus \{ - 1;1\}\)
\(\mathbb{R}\setminus \{0\}\)
\(\mathbb{R}\setminus \{ - 1;0\}\)
9000153802
Level:
A
Find the number of mutually different isosceles triangles (at least
two sides are equal) such that each side of each triangle is either
\(2\),
\(3\),
\(4\) or
\(5\).
\(14\)
\(16\)
\(17\)
\(24\)
9000375402
Level:
A
Find a set of the values of the real parameter
\(a\) which
ensure that the following equation does not have a solution.
\[
2x + a = a(a^{2} - x)
\]
\(\left \{-2\right \}\)
\(\left \{1\right \}\)
\(\left \{-1\right \}\)
\(\left \{0\right \}\)
9000153803
Level:
A
Find the number of mutually different triangles such that all
three sides of each triangle are mutually different and each side is
\(2\),
\(3\),
\(4\) or
\(5\).
\(3\)
\(4\)
\(14\)
\(16\)
9000375403
Level:
A
Find a set of the values of the real parameter
\(a\) which
ensure that the following equation has infinitely many solutions.
\[
a^{2}x + ax - a = 2x - 1
\]
\(\left \{1\right \}\)
\(\emptyset \)
\(\left \{0\right \}\)
\(\left \{-2\right \}\)
9000168701
Level:
A
Which of the given points is one of the vertices on the major axis of the ellipse \(9x^{2} + 16y^{2} - 18x + 96y + 9 = 0\)?
\([5;-3]\)
\([4;-3]\)
\([1;1]\)
\([1;0]\)