Solving Whole Integer Solutions for Easy Math Quesiton 3 (x^2)=a^2

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In summary, a whole integer is a positive or negative whole number that is not a fraction or decimal. Solving for integer solutions means finding values for variables in an equation that result in a whole number solution. To solve for integer solutions in an equation, you can use the method of taking the square root of both sides, resulting in two possible solutions, one positive and one negative. An equation can have multiple integer solutions, but there are exceptions, such as when there is a variable with an odd exponent, which will result in no integer solutions.
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W3pcq
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3(x^2)=a^2

When are a and x whole integers?
 
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  • #2
In what sense does this have anything to do with "Tensor Analysis and Differential geometry"? I'm moving it to "number theory".

In any case, if 3x2= a2 for a and x integers, then we must have
[itex]a= x\sqrt{3}[/itex] which is impossible unless x= a= 0. It implies [itex]\sqrt{3}= a/x[/itex] but [itex]\sqrt{3}[/itex] is irrational.

The only integer solution to 3x2= a2 is x= a= 0.
 

FAQ: Solving Whole Integer Solutions for Easy Math Quesiton 3 (x^2)=a^2

What is the easiest way to solve a whole integer solution for (x^2)=a^2?

The easiest way to solve this type of equation is by using the square root property. Since both x^2 and a^2 are perfect squares, you can simply take the square root of both sides to find the value of x.

What if a is a negative number?

If a is a negative number, you can still use the square root property. However, you will need to add a negative sign to the solution for x since (-a)^2 is equal to a^2.

Are there any other methods for solving this type of equation?

Yes, there are other methods such as factoring and completing the square. However, these methods may be more complex and time-consuming compared to using the square root property.

Can this type of equation have more than one solution?

Yes, in most cases, this type of equation will have two solutions. One positive and one negative, since the square root of a positive number can have both positive and negative values.

What if the equation is (x^2)=a?

If the equation is (x^2)=a, you can still use the square root property. In this case, the solution for x will be the square root of a, which can be a positive or negative number.

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