Question

(sgrt(10) - sgrt(2))^5 вычислить с помощью Бинома Ньютона,помогите,пожалуйста.

Answer 1

$(sqrt{10} - sqrt{2})^5\\ (a - b)^5 = a^5 - 5a^4b + 10a^3b^2 - 10a^2b^3 + 5ab^4 - b^5\\ a = sqrt{10}, b = sqrt{2}\\ (sqrt{10} - sqrt{2})^5 = (sqrt{10})^5 - 5(sqrt{10})^4sqrt{2} + 10(sqrt{10})^3(sqrt{2})^2 -\\- 10(sqrt{10})^2(sqrt{2})^3 + 5sqrt{10}(sqrt{2})^4 - (sqrt{2})^5 = 100sqrt{10} - 5 cdot 100 cdot sqrt{2} + \\ + 10cdot 10sqrt{10}2 - 10cdot 10cdot 2sqrt{2} + 5cdot sqrt{10}cdot 4 - 4sqrt{2} =$

$= sqrt{10}(100 + 200 +20) - sqrt{2}(500 + 200 + 4) = sqrt{10}(320) - sqrt{2}(704) =\\= sqrt{2}(320sqrt{5} - 704)$