Radical equations and inequalities

2010007704

Level:

Find the domain of the expression.

\sqrt{- x^{2} - 7 x + 30}

[- 10; 3]

(- \infty; - 10] \cup [3; \infty)

[- 3; 10]

\emptyset

2010007703

Level:

Find the domain of the expression.

\frac{1}{\sqrt{2 x^{2} - 11 x + 14}}

(- \infty; 2) \cup (\frac{7}{2}; \infty)

(2; \frac{7}{2})

(- \infty; 2] \cup [\frac{7}{2}; \infty)

[2; \frac{7}{2}]

2010007702

Level:

Find the solution of the equation.

\sqrt{x^{2} - 3 x + 6} = \sqrt{x^{2} - 4 x + 6}

x \in {0}

x \in \emptyset

x \in R

x \in R ∖ {0}

2010007701

Level:

Find the solution of the equation.

\sqrt{- 2 x^{2} + 3 x - 4} = 2

x \in \emptyset

x \in R

x \in (- 3; 3)

x \in {- 3; 3}

2000004609

Level:

Choose the correct statement about the following equation.

\sqrt{7 - \sqrt{x - 3}} = 2

The equation has just one root and the root is an even number.

The equation has no solution in

R

The equation has just one root and the root is an odd number.

The equation has just two roots.

2000004608

Level:

Choose the correct statement about the following equation.

\sqrt{x + 5} + \sqrt{2 - x} = 0

The equation has no solution in

R

The equation has just one root and the root is an odd number.

The equation has just one root and the root is an even number.

The equation has just two roots.

2000004607

Level:

Choose the correct statement about the following equation.

x - 2 \sqrt{x - 6} = 6

The roots of the equation are

x_{1} = 10

and

x_{2} = 6

The only root of the equation is

x = 6

The equation has no root in

R

The roots of the equation are

x_{1} = - 2

and

x_{2} = 6

2000004606

Level:

Choose the correct statement about the following equation.

5 + 2 \sqrt{x - 2} = 9

The solution of this equation is a number from the interval

(5; 6]

The solution of this equation is a number from the interval

(- 1; 0]

The solution of this equation is a number from the interval

(0; 3]

The solution of this equation is a number from the interval

(3; 5]

2000004605

Level:

Choose the correct statement about the following equation.

\sqrt{4 - x} = 3 - \sqrt{x - 4}

The equation has no solution in

R

The equation has just one root and the root is an odd number.

The equation has just one root and the root is an even number.

The equation has just two roots.

2000004604

Level:

Choose the correct statement about the following equation.

4 + 2 \sqrt{x + 4} = x

The root of the equation is

x = 12

The equation has no root in

R

The roots of the equation are

x_{1} = 0

and

x_{2} = 12

The roots of the equation are

x_{1} = 4

and

x_{2} = - 2

Radical equations and inequalities

2010007704

2010007703

2010007702

2010007701

2000004609

2000004608

2000004607

2000004606

2000004605

2000004604

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