- #1
oszust001
- 10
- 0
How can I solve that type of equation:
[tex]x^2+y^2=4z^2[/tex] or [tex]x^2+3y^2=4z^2[/tex]
[tex]x^2+y^2=4z^2[/tex] or [tex]x^2+3y^2=4z^2[/tex]
Given any values of x and y, we could then solve for z so these have an infinite number of solutions. Since you are asking for solutions in natural numbers, you could treat them as variations on the Pythagorean theorem and use the formulas for producing integer solutions to [itex]x^2+ y^2= z^2[/itex]: given any two integers, m and n, then [itex]x= m^2- n^2[/itex], [itex]y= 2mn[/itex], and [itex]z= m^2+ n^2[/itex], satisfy [itex]x^2+ y^2= z^2[/itex]. You would need to exempt some values of m and n to allow for the "3" and "4" coefficients.oszust001 said:How can I solve that type of equation:
[tex]x^2+y^2=4z^2[/tex] or [tex]x^2+3y^2=4z^2[/tex]
When we say "solve in natural numbers," it means finding a solution to a problem using only positive whole numbers (1, 2, 3, etc.) and excluding any fractions, decimals, or negative numbers.
Solving in natural numbers can help us find practical solutions to real-world problems. It also allows us to focus on the most relevant and meaningful solutions without getting distracted by complicated or irrelevant numbers.
Problems that involve counting, measuring, or categorizing can often be solved in natural numbers. This includes problems in mathematics, science, and other fields where whole numbers are used to represent quantities or values.
One common strategy is to use trial and error, where we try different combinations of numbers until we find a solution that works. Another strategy is to use patterns or relationships between numbers to find a solution. In some cases, we may also use mathematical formulas or equations to solve in natural numbers.
No, not all problems can be solved in natural numbers. Some problems may require the use of fractions, decimals, or negative numbers to find a solution. Additionally, some problems may not have a solution in natural numbers at all.