Math Formulas

Vene T. Bogoslavov: Collection of Solved Problems #2

MR-88 / 61.a

Simplify the following expression:

$a \sqrt{128}$

MR-89 / 87.b

Rationalize the denominator of the fraction:

$\frac{9}{\sqrt{12}}$

MR-90 / 92.a

Rationalize the denominator of the fraction:

$\frac{6}{\sqrt[3]{2}}$

MR-92 / 98.a

Rationalize the denominator of the fraction:

$\frac{1}{2 + \sqrt{3}}$

MR-96 / 100.a

Hozza egyszerűbb alakra a következő kifejezést:

$\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}$

MR-85 / 221.a

Simplify the following expression:

$\frac{\sqrt{x} + \sqrt{y} - 1}{x + \sqrt{x y}} + \frac{\sqrt{x} - \sqrt{y}}{2 \sqrt{x y}} (\frac{\sqrt{y}}{x - \sqrt{x y}} + \frac{\sqrt{y}}{x + \sqrt{x y}})$

$x > 0; y > 0$

MR-95 / 230.b

Simplify the following expression:

$\sqrt{6 - 4 \sqrt{2}}$

MR-91 / 336.

Simplify the following expression:

$(\sqrt[3]{1 + 2 \sqrt{6}} - \sqrt[6]{25 + 4 \sqrt{6}}) \cdot \sqrt[3]{2 \sqrt{6} - 1}$

MR-115 / 382.a

Simplify the following expression:

$\frac{2 + i}{2 - i} + \frac{2 - i}{2 + i}$

MR-200 / 1069.a

Solve the exponential equation:

$2^{x - 3} = 16$

MR-202 / 1070.a

Solve the following exponential equation:

$16^{\frac{1}{x}} = 4^{\frac{x}{2}}$

MR-204 / 1071.b

Solve the following exponential equation:

$4^{x + 1} + 4^{x} = 320$

MR-205 / 1073.

Solve the following exponential equation:

$2^{x - 1} - 2^{x - 3} = 3^{x - 2} - 3^{x - 3}$

MR-208 / 1076.a

$5^{x} - 5^{3 - x} = 20$

MR-185 / 1353.

Prove the following identity::

$s i n^{4} α + c o s^{2} α + s i n^{2} α \cdot c o s^{2} α = 1$