- #1
madah12
- 326
- 1
Homework Statement
what's the best way solving question of finding two positive rational a and b given c
where a +b*sqrt2= an irrational number c
HallsofIvy said:In general, such a problem will NOT have a solution. For example, there exist no rational a, b, such that [itex]a+ b\sqrt{2}= \pi[/itex].
The purpose of solving this equation is to find the values of A and b (positive rational numbers) that will make the equation true when multiplied by the irrational number sqrt2. This type of equation is common in mathematics and can be used to simplify expressions or solve real-world problems.
Yes, it is possible to solve this equation with positive rational numbers. However, the solutions may not always be unique and may require some trial and error to find the correct values for A and b.
The process for solving this equation involves isolating the irrational term (sqrt2) on one side of the equation and the rational terms (A and b) on the other side. Then, using properties of rational and irrational numbers, we can manipulate the equation to solve for the values of A and b.
Yes, in order for the equation to have a positive rational solution, A and b must be positive rational numbers. If either of these values is negative or irrational, the equation will not have a positive rational solution.
This type of equation can be used in various real-world applications, such as calculating the diagonal of a square with rational side lengths, finding the hypotenuse of a right triangle with rational side lengths, or solving problems in geometry or physics that involve irrational numbers.