Question

6x3y4 – xy – 3x4y ≥ 0

Answer 1

Ответ:72xy-xy-12xy>0

59xy>0

xy>0

Объяснение:1000000000000000000000000000000%

Answer 2

To solve the inequality 6x3y4 – xy – 3x4y ≥ 0, we can factor out common terms to simplify it. The equation becomes:

xy(6y^3 - 1) - 3x^4y ≥ 0

Now, we can analyze the sign of each factor individually.

For xy, the sign depends on the values of x and y. If both x and y are positive or both are negative, xy will be positive. If one of them is negative and the other is positive, xy will be negative.

For 6y^3 - 1, let's examine the critical points. Setting 6y^3 - 1 = 0, we have:

6y^3 = 1 y^3 = 1/6 y = (1/6)^(1/3)

The value of (1/6)^(1/3) is approximately 0.628.

By plotting a number line and including the critical point at y ≈ 0.628, we can determine the sign of 6y^3 - 1 in different intervals:

Interval 1: (-∞, 0.628) In this interval, 6y^3 - 1 is negative.

Interval 2: (0.628, +∞) In this interval, 6y^3 - 1 is positive.

Now, let's combine the signs of xy and 6y^3 - 1 based on the intervals:

Interval 1: (-∞, 0.628) In this interval, xy is negative, and 6y^3 - 1 is negative. The product of a negative and a negative is positive.

Interval 2: (0.628, +∞) In this interval, xy is positive, and 6y^3 - 1 is positive. The product of a positive and a positive is positive.

To satisfy the inequality 6x3y4 – xy – 3x4y ≥ 0, the expression must be positive or zero.

Therefore, the solution to the inequality is:

(-∞, 0.628] ∪ [0, +∞)