Question

Y^3-27y^2-(y-9)^3>0

Answer 1

Ответ:

y = 3

Объяснение:

y³ - 27y² - (y - 9)³ > 0

y³ - 27y² - y³ + 27y² - 243y + 729 > 0

-243y + 729 > 0

y = 3

Ответ: y = 3

Answer 2

To solve the inequality $y^3 - 27y^2 - (y - 9)^3 > 0$, we can simplify and factorize the expression first.

Expanding $(y - 9)^3$ using the binomial expansion formula, we have:

$(y - 9)^3 = y^3 - 3y^2 \cdot 9 + 3y \cdot 9^2 - 9^3$ $= y^3 - 27y^2 + 243y - 729$

Substituting this back into the inequality, we get:

$y^3 - 27y^2 - (y - 9)^3 > 0$ $y^3 - 27y^2 - (y^3 - 27y^2 + 243y - 729) > 0$ $y^3 - 27y^2 - y^3 + 27y^2 - 243y + 729 > 0$ $-243y + 729 > 0$ $-243y > -729$ $y < \frac{-729}{-243}$ $y < 3$

Therefore, the solution to the inequality $y^3 - 27y^2 - (y - 9)^3 > 0$ is $y < 3$.