Question

Решите 14 номер. Нужно полное решение.

Answer 1

$c+\frac{1}{c}=5 \\\\\frac{c^{2}+1 }{c}=5\\\\(\frac{c^{2}+1 }{c})^{3} =5^{3}\\\\\frac{c^{6}+3c^{4}+3c^{2}+1 }{c^{3}} =125\\\\\frac{c^{6}+1 }{c^{3}}+\frac{3c^{2}(c^{2}+1)}{c^{3}}=125\\\\\frac{c^{6}+1 }{c^{3}}+\frac{3(c^{2}+1) }{c}=125\\\\\frac{c^{6}+1 }{c^{3}}=125-3*\frac{c^{2}+1 }{c}\\\\\frac{c^{6}+1 }{c^{3}}=125-3*5\\\\\frac{c^{6}+1 }{c^{3}}=110\\\\Otvet:\boxed{110}$