10.7

Part of IV Soros Olympiad 1997 - 98 (Russia)

Problems(2)

(\sqrt2+\sqrt3+\sqrt5)^1997 (IV Soros Olympiad 1997-98 Correspondence 10.7)

Source:

Prove that the number

\left(\sqrt2+\sqrt3+\sqrt5\right)^{1997}

can be represented as

A\sqrt2+B\sqrt3+C\sqrt5+D\sqrt{30}

A

B

C

D

are integers. Find with approximation to

10^{-10}

\frac{D}{A}

algebraRadicals

6\sqrt2 sinx tgx - 2\sqrt2 tgx +3sinx -1=0 (IV Soros Olympiad 1997-98 R3 10.7)

Source:

How many different solutions on the interval

[0, \pi]

does the equation

6\sqrt2 \sin x \cdot tgx - 2\sqrt2 tgx +3\sin x -1=0

algebratrigonometry