Question

3y^2 + 7y + 4 <0; 9у^2 - 6у +1 < 0;3у^2-6у+3>0​

Answer 1

Ответ:

$y e ( - \frac{4}{3} - 1)$

Это ответ на 1-ое уровнения

Answer 2

To solve these inequalities, let's work through them one by one:

1. $3y^2 + 7y + 4 < 0$:

This quadratic inequality involves a quadratic expression $3y^2 + 7y + 4$. To solve it, we need to find the values of $y$ for which the expression is less than zero.

First, let's factor the quadratic expression: $3y^2 + 7y + 4 = (3y + 4)(y + 1)$.

Now, set each factor equal to zero and solve for $y$: $3y + 4 = 0$ => $y = -4/3$ $y + 1 = 0$ => $y = -1$

These values of $y$ divide the number line into three intervals: $(-\infty, -4/3)$, $(-4/3, -1)$, and $(-1, \infty)$.

Now, we can test a value from each interval in the original inequality to determine the sign of the expression in that interval. For example, testing $y = -2$: $3(-2)^2 + 7(-2) + 4 = 12 - 14 + 4 = 2 < 0$.

Since the expression is negative in the interval $(-4/3, -1)$, the solution to $3y^2 + 7y + 4 < 0$ is $(-4/3, -1)$.

2. $9y^2 - 6y + 1 < 0$:

This quadratic inequality involves the quadratic expression $9y^2 - 6y + 1$. Let's solve it similarly.

First, factor the quadratic expression: $9y^2 - 6y + 1 = (3y - 1)^2$.

Setting the factor equal to zero: $3y - 1 = 0$ => $y = 1/3$.

The solution is $y = 1/3$, but since this expression is a perfect square, it is always non-negative. Therefore, there are no values of $y$ that satisfy $9y^2 - 6y + 1 < 0$.

3. $3y^2 - 6y + 3 > 0$:

This quadratic inequality involves the quadratic expression $3y^2 - 6y + 3$. Let's solve it.

Divide the entire inequality by 3: $y^2 - 2y + 1 > 0$.

Factor the quadratic expression: $y^2 - 2y + 1 = (y - 1)^2$.

Setting the factor equal to zero: $y - 1 = 0$ => $y = 1$.

The solution is $y = 1$, but since this expression is a perfect square, it is always non-negative. Therefore, there are no values of $y$ that satisfy $3y^2 - 6y + 3 > 0$.

In summary:

1. $3y^2 + 7y + 4 < 0$ has a solution of $(-4/3, -1)$.
2. $9y^2 - 6y + 1 < 0$ has no solution.
3. $3y^2 - 6y + 3 > 0$ has no solution.