1003187203
Level:
C
How many solutions does the equation \( \sqrt{x^2-4x+4}=|x| \) have?
\( 1 \)
\( 2 \)
\( 0 \)
\( 3 \)
Radical Equations and Inequalities
1003187202
Level:
C
Which of following equalities is true for all real numbers \( x \)?
\( \sqrt{(x-3)^2} = |x-3| \)
\( |-x| = x \)
\( |x-1|=x-1 \)
\( \sqrt{x^2} = x \)
1003187201
Level:
A
If \( \sqrt{x^2-8x+16}=4-x \), then the number \( x \) can be equal to:
\( -2 \)
\( 10 \)
\( 6 \)
\( 8 \)
1003020604
Level:
A
Find the domain of the expression.
\[
\frac{\sqrt{-x^2-2x+24}}{2x^2-3x+3}
\]
\(\left[-6,4\right]\)
\(\left[-4,6\right]\)
\(\mathbb{R}\setminus\left[-6,4\right]\)
\(\mathbb{R}\setminus\left[-4,6\right]\)
1003020603
Level:
A
Find the domain of the expression.
\[
\sqrt{-x^2+x+20}
\]
\(\left[-4,5\right]\)
\(\left(-\infty,-4\right]\cup\left[5,\infty\right)\)
\(\emptyset\)
\(\left[-5,4\right]\)
1003020602
Level:
A
Find the domain of the expression.
\[
\frac{\sqrt{x^2-x-6}}{x^2-7x+10}
\]
\(\left(-\infty,-2\right]\cup\left[3,5\right)\cup\left(5,\infty\right)\)
\(\left(-\infty,-2\right)\cup\left(3,\infty\right)\)
\(\left(-\infty,-2\right)\cup\left(3,5\right)\cup\left(5,\infty\right)\)
\(\left(-\infty,2\right)\cup\left(3,5\right)\cup\left(5,\infty\right)\)
1003020601
Level:
A
Find the domain of the expression.
\[
\frac1{\sqrt{5x^2+7x-6}}
\]
\(\left(-\infty,-2\right)\cup\left(\frac35,\infty\right)\)
\(\left(-2,\frac35\right)\)
\(\left(-\infty,-2\right]\cup\left[\frac35,\infty\right)\)
\(\left[-2,\frac35\right]\)
1003020702
Level:
B
Find the solution of the inequality.
\[
\sqrt{3x^2-x+7}\geq2
\]
\(x\in\mathbb{R}\)
\(x\in\emptyset\)
\(x\in\left(-\frac13,\frac73\right)\)
\(x\in\mathbb{R}\setminus\{2\}\)
1003020701
Level:
B
Find the solution of the inequality.
\[
\sqrt{-2x^2+x+5}\geq5
\]
\(x\in\emptyset\)
\(x\in[-1,5]\)
\(x\in\left(-\frac12,\frac52\right)\)
\(x\in\mathbb{R}\)
1003019902
Level:
A
Find the solution of the equation.
\[
\sqrt{x^2-4x+3}=\sqrt{x^2-6x+3}
\]
\(x\in\{0\}\)
\(x\in\mathbb{R}\)
\(x\in\emptyset\)
\(x\in\mathbb{R}\setminus\{0\}\)