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9000086708

Level:

Identify the equation which arises from the following equation using an optimal substitution. \[ \mathop{\mathrm{tg}}\nolimits ^{2}v -\mathop{\mathrm{cotg}}\nolimits ^{-1}v = 2 \]

\(t^{2} - t - 2 = 0\)

Equation is not convenient for a substitution.

\(t^{2} + t = 0\)

\(\mathop{\mathrm{tg}}\nolimits t = 2\)

9000085609

Level:

Given the number \(45\: 875\), round this number to nearest thousands, nearest hundreds and subtract the results.

\(100\)

\(200\)

\(1\: 000\)

\(0\)

9000085603

Level:

Find the sum of the three numbers obtained by rounding the number \(5\: 316\) to the nearest tens, hundreds and thousands.

\(15\: 620\)

\(15\: 610\)

\(15\: 560\)

\(15\: 580\)

9000083703

Level:

Find all the values of \(x\in \mathbb{R}\) for which the given expression equals zero. \[ \frac{x^{3} - x} {x - 1} \]

\(x = -1,\ x = 0\)

\(x = 0\)

\(x = 1\)

\(x = -1,\ x = 0,\ x = 1\)

9000083704

Level:

Find all the values of \(x\in \mathbb{R}\) for which the given expression equals zero. \[ \frac{x^{2} - 4x + 4} {x(x - 2)} \]

The expression never equals zero.

\(x = 0\)

\(x = 2\)

\(x = -2,\ x = 0\)

9000083705

Level:

Find all the values of \(x\in \mathbb{R}\) for which the given expression equals zero. \[ \frac{2x(x + 2)(x - 3)} {x^{2} - 4} \]

\(x = 0,\ x = 3\)

\(x = -2,\ x = 0,\ x = 3\)

\(x = 0\)

\(x =\pm 2\)

9000083706

Level:

Find all the values of \(x\in \mathbb{R}\) for which the given expression equals zero. \[ \frac{4x^{2} - 36} {4x^{2} + 24x + 36} \]

\(x = 3\)

\(x = 4\)

\(x = -3,\ x = 3\)

The expression never equals zero.

9000083707

Level:

Find all the values of \(x\in \mathbb{R}\) for which the given expression equals zero. \[ \frac{4x^{3} + 20x^{2} + 25x} {x + 1} \]

\(x = 0,\ x = -\frac{5} {2}\)

\(x = 0\)

\(x = -\frac{5} {2}\)

\(x = -1\)

9000083708

Level:

Find all the values of \(x\in \mathbb{R}\) for which the given expression equals zero. \[ \frac{x^{2} - (2x - 1)^{2}} {x^{2} - 4} \]

\(x = \frac{1} {3},\ x = 1\)

\(x = -\frac{1} {3},\ x = 1\)

\(x =\pm 2\)

\(x = 1\)

9000083709

Level:

Find all the values of \(x\in \mathbb{R}\) for which the given expression equals zero. \[ \frac{(2x + 3)^{2} - (3x - 2)^{2}} {x - 5} \]

\(x = -\frac{1} {5}\)

\(x = 5\)

\(x = -5\)

\(x = \frac{1} {5}\)

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