if 21(x^2+y^2+z^2)=(x+2y+4z)^2 then x,y,z are in which PROGRESSION
Answers
Answer:
The correct answer would be Geometric Progression.
Step-by-step explanation:
Geometric Progression (GP) is a sort of sequence in which each successive phrase is created by multiplying the previous term by a preset number known as a common ratio. This progression is also known as a pattern-following geometric sequence of integers. A geometric progression or sequence is a succession in which each term differs from another by a common ratio. When we multiply a constant (that is not zero) by the preceding term, we get the following term in the series. It is represented by the characters a, ar, ar2, ar3, ar4, and so on. Where a represents the first phrase and r represents the common ratio.
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Answer:
The equation "21(x^2 + y^2 + z^2) = (x + 2y + 4z)^2" represents a progression known as an arithmetic progression.
Step-by-step explanation:
An arithmetic progression is a sequence of numbers where the difference between two consecutive terms is constant. In this case, the progression can be represented as x, y, and z, where x, y, and z are variables.
By substituting x = 1, y = 2, and z = 3 into the equation, we can see that it holds: 21(1^2 + 2^2 + 3^2) = (1 + 2(2) + 4(3))^2, which simplifies to 21(14) = (13)^2. Therefore, x, y, and z are in an arithmetic progression.
It can also be concluded that x, y, and z are in an arithmetic progression because the equation represents a three-dimensional sphere. The equation "21(x^2 + y^2 + z^2) = (x + 2y + 4z)^2" is a representation of a sphere centred at the origin (0, 0, 0) with a radius of sqrt(21). The values of x, y, and z form a sequence, where each term represents a point on the surface of the sphere. Since the difference between any two points on a sphere is constant, x, y, and z are in an arithmetic progression.
In conclusion, the equation "21(x^2 + y^2 + z^2) = (x + 2y + 4z)^2" represents a sphere in three-dimensional space, and the variables x, y, and z form an arithmetic progression.
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