Question

Найдите значение выражения y^4 + 2у^2 - 5у + 1 при у = 1/2.

Answer 1

y⁴ + 2y² - 5y + 1 = (y⁴ + 2y² + 1) - 5y = (y² + 1)² - 5y

$y=\frac{1}{2}\\\\(y^{2}+1)^{2} -5y=((\frac{1}{2})^{2}+1)^{2}-5*\frac{1}{2}=(\frac{1}{4}+1)^{2}-\frac{5}{2}=(\frac{5}{4})^{2}-\frac{5}{2}=\frac{25}{16}-\frac{40}{16}=-\frac{15}{16}=-\frac{15}{16}=-0,9375$

Answer 2

y⁴ + 2y² - 5y + 1 = (1/2)⁴ + 2·(1/2)² - 5·(1/2) + 1 = 1/16 + 1/2 - 2,5 + 1 = -0,9375