Question

X^2+y^2+z^2-3x+5y-4z=0

Answer 1

Ответ:

x=3 y=-5 z=4

Пошаговое объяснение:

можно записать как:

x(x-3)+y(y+5)+z(z-4)=0

x-3 =0 y+5=0 z-4=0

x=3 y=-5 z=4

Answer 2

The equation you've provided represents a three-dimensional geometric object called a sphere. It is defined by the equation:

x^2 + y^2 + z^2 - 3x + 5y - 4z = 0

To analyze the properties of this sphere, let's rewrite the equation in standard form:

x^2 - 3x + y^2 + 5y + z^2 - 4z = 0

Completing the square for each variable, we can rewrite the equation as:

(x^2 - 3x + 9/4) + (y^2 + 5y + 25/4) + (z^2 - 4z + 4) = 9/4 + 25/4 + 4

Simplifying, we have:

(x - 3/2)^2 + (y + 5/2)^2 + (z - 2)^2 = 9/4 + 25/4 + 16/4

(x - 3/2)^2 + (y + 5/2)^2 + (z - 2)^2 = 50/4 + 16/4

(x - 3/2)^2 + (y + 5/2)^2 + (z - 2)^2 = 66/4

(x - 3/2)^2 + (y + 5/2)^2 + (z - 2)^2 = 33/2

From this form, we can determine the center and radius of the sphere. The center of the sphere is located at (3/2, -5/2, 2), and the radius is the square root of 33/2.

Therefore, the equation x^2 + y^2 + z^2 - 3x + 5y - 4z = 0 represents a sphere centered at (3/2, -5/2, 2) with a radius of √(33/2).