Question

625(-625-x²) ≤(-625-x²)x²

Answer 1

Ответ:

x∈[-25;25]

Объяснение:

625(-625-x²) ≤(-625-x²)x²

625(-625-x²) -(-625-x²)x²≤0

(-625-x²)(625-x²)≤0

(625+x²)(x²-625)≤0

(625+x²)(x-25)(x+25)≤0

выражение в первой скобке >0 ,

так как квадрат любого числа есть число неотрицательное

(x-25)(x+25)≤0

решаем методом интервалов

нули : -25;   25

++++[-25]--------[25]+++++

Ответ: x∈[-25;25]

Answer 2

Ответ: во вложении Объяснение:

Answer 3

Let's solve the given inequality step by step:

625(-625 - x²) ≤ (-625 - x²)x²

First, let's simplify both sides of the inequality:

-390,625 - 625x² ≤ -625x² - x⁴

Next, let's collect like terms and bring all terms to one side of the inequality:

0 ≤ -x⁴ - 390,625

Now, we can multiply both sides by -1 to flip the inequality:

0 ≥ x⁴ + 390,625

Since the left side is zero, we can remove it from the inequality:

x⁴ + 390,625 ≤ 0

The left side is a sum of squares, so it will always be greater than or equal to zero. Therefore, there are no real solutions to this inequality.

In summary, the inequality 625(-625 - x²) ≤ (-625 - x²)x² does not have any real solutions.