Problems

Age
Difficulty
Found: 15

The student did not notice the multiplication sign between two three-digit numbers and wrote one six-digit number, which turned out to be seven times bigger than their product. Determine these numbers.

The student did not notice the multiplication sign between two seven-digit numbers and wrote one fourteen-digit number, which turned out to be three times bigger than their product. Determine these numbers.

How many rational terms are contained in the expansion of

a) \((\sqrt 2 + \sqrt[4]{3})^{100}\);

b) \((\sqrt 2 + \sqrt[3]{3})^{300}\)?