2000004601
Level:
A
Solve the following equation.
\[ \sqrt{x^2+2x+5} =x+3\]
\( x=-1\)
\( x=-2\)
\( x=2\)
\( x=1\)
Radical equations and inequalities
2000004610
Level:
A
Choose the correct statement about the following equation.
\[ \sqrt{(x+5)^2} =x+5\]
The solution of the equation are all \( x \in [ -5; \infty) \).
The solution of the equation are all \( x \in \mathbb{R} \).
The equation has no solution in \(\mathbb{R} \).
The equation has just one root \( x=0\).
Radical Equations
Submitted by ladislav.foltyn on Thu, 03/14/2019 - 19:411003177803
Level:
C
Choose the domain of the expression.
\[ \frac1{\sqrt{|3x-9|-\sqrt2}} \]
\( \left(-\infty;3-\frac{\sqrt2}3\right)\cup\left(3+\frac{\sqrt2}3;\infty\right) \)
\( \left(-\infty;-3-\frac{\sqrt2}3\right)\cup\left(3+\frac{\sqrt2}3;\infty\right) \)
\( \left(-\infty;-3+\frac{\sqrt2}3\right)\cup\left(3+\frac{\sqrt2}3;\infty\right) \)
\( \left(-\infty;-3-\frac{\sqrt2}3\right)\cup\left(-3+\frac{\sqrt2}3;\infty\right) \)
1003177801
Level:
C
Choose the domain of the expression \( \sqrt{|x-3|-4} \).
\( (-\infty;-1]\cup[7;\infty) \)
\( (-1;3]\cup[7;\infty) \)
\( [7;\infty) \)
\( (-\infty;1)\cup(7;\infty) \)
1003187204
Level:
C
The solution set of the equation \( \sqrt{x^2-2x+1}-2|x+3|+x+7=0 \) is:
\( \{-7\}\cup[1;+\infty) \)
\( \{-7\}\cup(1;+\infty) \)
\( [1;+\infty) \)
\( (1;+\infty) \)
1003187203
Level:
C
How many solutions does the equation \( \sqrt{x^2-4x+4}=|x| \) have?
\( 1 \)
\( 2 \)
\( 0 \)
\( 3 \)
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.
\[
\frac{\sqrt{-x^2-2x+24}}{2x^2-3x+3}
\]
\(\left[-6;4\right]\)
\(\left[-4;6\right]\)
\(\mathbb{R}\setminus\left[-6;4\right]\)
\(\mathbb{R}\setminus\left[-4;6\right]\)