Question

A, b, c действительные числа определите знаки чисел(+ или -) если a^3b^2>0 ac^3<0 abc>0

Answer 1

Ответ на картинке внизу

Answer 2

To determine the signs of the numbers A, B, and C, let's analyze each inequality given:

1. a^3 * b^2 > 0: Since the product of two positive numbers is positive, we can conclude that both a^3 and b^2 have the same sign (both positive).

2. ac^3 < 0: The product of two numbers with opposite signs is negative. Therefore, we can deduce that 'a' and 'c^3' have opposite signs (one positive and the other negative).

3. abc > 0: The product of three positive numbers is positive. So, all three variables 'a', 'b', and 'c' have the same sign (all positive).

Now, combining the information:

From statement 1, we know that 'a^3' and 'b^2' have the same sign (both positive).

From statement 2, we know that 'a' and 'c^3' have opposite signs (one positive and the other negative).

From statement 3, we know that 'a', 'b', and 'c' have the same sign (all positive).

Since 'a' appears in all three statements, let's analyze its sign:

1. 'a^3' and 'b^2' have the same sign (both positive). So, 'a' must be positive.

2. 'a' and 'c^3' have opposite signs. We already established that 'a' is positive, so 'c^3' must be negative. Consequently, 'c' must be negative.

3. 'a', 'b', and 'c' have the same sign (all positive). Since we determined that 'a' is positive and 'c' is negative, 'b' must also be positive.

To summarize:

A (a) is positive. B (b) is positive. C (c) is negative.