Question

10x2−18x+8<0 Help me please....​

Answer 1

Ответ:

(4/5;1)

Объяснение:

Решим через дискриминант

D = 18^2-4*10*8 = 4

х = 18 + 2/20 = 1

х = 18 - 2/20 = 4/5

Ответ : х принадлежит (4/5;1)

Answer 2

To solve the inequality $10x^2 - 18x + 8 < 0$, you can use factoring and the concept of interval notation. Here are the steps:

1. First, factor the quadratic expression:

$10x^2 - 18x + 8 = 2x^2 - 9x + 4x - 8 = 2x(x - 4) - 1(4x - 8) = 2x(x - 4) - 4(x - 2)$

2. Now, the inequality becomes:

$2x(x - 4) - 4(x - 2) < 0$

3. Next, identify the critical points by setting each factor equal to zero:

For $2x(x - 4) - 4(x - 2) = 0$, we have two critical points:

$2x(x - 4) = 4(x - 2)$

$2x(x - 4) - 4(x - 2) = 0$

Now, solve for $x$:

$2x(x - 4) = 4(x - 2)$

$2x^2 - 8x = 4x - 8$

$2x^2 - 8x - 4x + 8 = 0$

$2x^2 - 12x + 8 = 0$

Divide by 2 to simplify:

$x^2 - 6x + 4 = 0$

Now, factor this quadratic equation:

$(x - 4)(x - 2) = 0$

So, the critical points are $x = 4$ and $x = 2$.

4. You now have three intervals: $(-∞, 2)$, $(2, 4)$, and $(4, ∞)$. These intervals are determined by the critical points.

5. To determine the sign of the expression in each interval, choose a test point from each interval and plug it into the original inequality. You can use $x = 0$ for the first interval, $x = 3$ for the second interval, and $x = 5$ for the third interval.

• For the interval $(-∞, 2)$, let's use $x = 0$:

$10(0)^2 - 18(0) + 8 = 8 > 0$

• For the interval $(2, 4)$, let's use $x = 3$:

$10(3)^2 - 18(3) + 8 = 10(9) - 54 + 8 = 90 - 54 + 8 = 44 > 0$

• For the interval $(4, ∞)$, let's use $x = 5$:

$10(5)^2 - 18(5) + 8 = 10(25) - 90 + 8 = 250 - 90 + 8 = 168 > 0$

6. Now, based on the signs in each interval:

• $(-∞, 2)$: The expression is positive (+).
• $(2, 4)$: The expression is positive (+).
• $(4, ∞)$: The expression is positive (+).

The inequality $10x^2 - 18x + 8 < 0$ is not satisfied in any of the intervals, and therefore, there are no solutions. The solution is an empty set or "no solution."