Question

(x^2 -6x)^5>=(2x-7)^5

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

Рассмотрим случаи, когда основание равно и не равно нулю.

Если равно нулю 2х-7=0, то 2х=7, х=3,5

При этом значении правая часть равна нулю, а левая 3,5²-6*3,5=

12,25- 21 =-8,75- отрицательна, неравенство не выполняется.

Поэтому, поделив обе части неравенства на неравное нулю число

((х²-6х)/(2х-7))⁵≥1

((х²-6х)/(2х-7)≥1

(х²-6х-2х+7)/(2х-7)≥0

(х²-8х+7)/(2х-7)≥ 0равносильно неравенству

(х-1)(х-7)*(2х-7)≥0, при условии х≠3,5

Используя метод интервалов, точки 1; 3,5; 7 разделят на интервалы числовую ось, определим знаки в каждом промежутке и отберем неотрицательный ответ, при условии, что х≠3,5

Получим ответ х∈[1;3,5)∪[7;+∞)

Answer 3

To solve the inequality $(x^2 - 6x)^5 \geq (2x - 7)^5$, we need to find the values of $x$ that satisfy the inequality. Here's how we can do it step by step:

Step 1: Expand both sides of the inequality:

$(x^2 - 6x)^5 = x^{10} - 30x^9 + 360x^8 - 2160x^7 + 6480x^6 - 7776x^5$

$(2x - 7)^5 = 32x^5 - 160x^4 + 320x^3 - 280x^2 + 98x - 7$

Step 2: Rewrite the inequality:

$x^{10} - 30x^9 + 360x^8 - 2160x^7 + 6480x^6 - 7776x^5 \geq 32x^5 - 160x^4 + 320x^3 - 280x^2 + 98x - 7$

Step 3: Move all terms to one side of the inequality:

$x^{10} - 30x^9 + 360x^8 - 2160x^7 + 6452x^6 - 7616x^5 + 160x^4 - 320x^3 + 280x^2 - 98x + 7 \geq 0$

Step 4: Now, we need to find the critical points, which are the values of $x$ that make the expression equal to zero. To do this, we can set the left-hand side expression equal to zero and solve for $x$:

$x^{10} - 30x^9 + 360x^8 - 2160x^7 + 6452x^6 - 7616x^5 + 160x^4 - 320x^3 + 280x^2 - 98x + 7 = 0$

Unfortunately, solving this polynomial equation for $x$ is not straightforward and cannot be done algebraically. We would need to use numerical methods to find approximate solutions.

Step 5: Analyze the regions between the critical points:

Once we have the critical points, we can divide the real number line into intervals using these critical points. In each interval, we need to determine whether the expression $(x^2 - 6x)^5$ is greater than or equal to $(2x - 7)^5$.

However, since finding the critical points involves numerical methods, I'm unable to provide you with exact solutions to the inequality. If you have specific values for $x$ or if you're interested in the general behavior of the inequality, I can assist with further analysis.