Question

Решите неравенство (3x-8)^2 (8x-3)^2

Answer 1

(3x-8)²*(8x-3)²>0

Так как (3x-8)²≥0 и (8x-3)≥0     ⇒

3x-8≠0     3x≠8  |÷3       x≠8/3≠2²/₃.

8x-3≠0   8x≠3  |÷8        x≠3/8.

Ответ: x∈(-∞;3/8)U(3/8;2²/₃)U(2²/₃;+∞).

Answer 2

To solve the inequality, I assume you want to find the values of x for which the expression is greater than or equal to zero (i.e., the expression is non-negative). To do this, we need to consider the signs of each factor in the expression.

Let's break down the factors:

1. (3x - 8)^2: This expression will be non-negative for all values of x because it's squared.

2. (8x - 3)^2: This expression will also be non-negative for all values of x because it's squared.

Since the product of two non-negative factors is always non-negative, we can conclude that the entire expression is non-negative for all values of x.

In interval notation, the solution to the inequality is: x ∈ (-∞, +∞) or simply all real numbers.