Question

(x+1)(x^2+1)(x^4+1)-1/5x^8
Если
X=6

Answer 1

a² - b² = (a - b)(a + b)

(x+1)(x^2+1)(x^4+1)-1/5x^8

Если

X=6

x - 1 ≠ 0 домножим числитель и знаменатель

(x+1)(x^2+1)(x^4+1) = (x - 1)(x + 1)(x^2 + 1)(x^4 + 1)/(x - 1) = (x^2 - 1)(x^2 + 1)(x^4 + 1)/(x - 1) = (x^4 - 1)(x^4 + 1) / (x - 1) = (x^8 - 1) / (x - 1)

x - 1 = 5 при x = 6

(x^8 - 1)/5 - x^8/5 = x^8/5 - 1/5 - x^8/5 = -1/5

ответ -1/5

$(x + 1)(x^{2} + 1)(x^{4} + 1) = (x + 1)(x^{2} + 1)(x^{4} + 1)(x - 1) / (x - 1) = (x^2 - 1)(x^2 + 1)(x^4 + 1)/(x - 1) = (x^4 - 1)(x^4 + 1)/(x - 1) = (x^8 - 1)/(x - 1)\\x = 6\\\\x - 1 = 5\\(x^8 - 1)/5 - x^8/5 = x^8/5 - 1/5 - x^8/5 = -1/5$