- #1

cacosomoza

- 11

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Pretty simple, how do I prove (x^2)>0 ?

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- Thread starter cacosomoza
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In summary, to prove that (x^2)>0, we can use the property that a positive real times a positive real is greater than 0 and a negative real times a negative real is greater than 0. Additionally, we can use the requirement for any "ordered field" that states "if a< b and c> 0, then ac< bc" and apply it to the case of a= 0, b= x, and c= x. This holds true for all real numbers except for x= 0, where the statement is undefined.

- #1

cacosomoza

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Pretty simple, how do I prove (x^2)>0 ?

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- #2

jegues

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cacosomoza said:Pretty simple, how do I prove (x^2)>0 ?

Why not use induction and try to prove it?

- #3

cacosomoza

- 11

- 0

x belongs to R, not N, so I cannot apply induction

- #4

fluxions

- 51

- 0

Try using this property: If x < y and z > 0, then xz < yz, examining each case separately.

- #5

JonF

- 621

- 1

Well how you wrote it, it isn’t true since 0^2 = 0. You probably meant x^2 ≥ 0.cacosomoza said:Pretty simple, how do I prove (x^2)>0 ?

Since this is in the calculus and beyond forum do you know how to find minima for a function?

EDIT:

Or you could use the properties: that a positive real times a positive real is greater than 0, a negative real times a negative real is greater than 0.

- #6

HallsofIvy

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- #7

JonF

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slickHallsofIvy said:

The purpose of proving (x^2)>0 is to show that the square of any real number is always positive. This is a fundamental concept in mathematics and is used in many mathematical proofs and equations.

It is important to prove (x^2)>0 because it helps us understand the properties of real numbers and their relationship to each other. It also allows us to solve equations and inequalities involving squares.

To prove (x^2)>0, we first start by assuming that x is a real number. Then, we square x and use algebraic manipulation to show that the result is always positive. This can be done by factoring, completing the square, or using the quadratic formula.

No, there are no exceptions to (x^2)>0 being true. This is a universal property of real numbers and is always true, regardless of the value of x.

Proving (x^2)>0 is useful in real life when dealing with quantities that can never be negative, such as distance, area, or time. It also helps in understanding the behavior of quadratic equations and their solutions.

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