Finding Triples to Satisfy $\frac{5}{2}$

  • MHB
  • Thread starter anemone
  • Start date
In summary, finding triples to satisfy $\frac{5}{2}$ means finding three numbers that, when multiplied together, equal $\frac{5}{2}$. It can be important in various mathematical and scientific applications, and can be found using techniques such as trial and error or algebraic manipulation. There can be multiple sets of triples that satisfy $\frac{5}{2}$, and these triples can be negative or fractions.
  • #1
anemone
Gold Member
MHB
POTW Director
3,883
115
Find all triples $(a,\,b,\,c)$ of positive integers such that $\dfrac{a}{b}+\dfrac{c}{a}+\dfrac{b}{c+1}=\dfrac{5}{2}$.
 
Last edited:
Mathematics news on Phys.org
  • #2
anemone said:
Find all triples $(a,\,b,\,c)$ of positive integers such that $\dfrac{a}{b}+\dfrac{c}{a}+\dfrac{b}{z+1}=\dfrac{5}{2}$.

what s z ?
 
  • #3
It's a typo...$z$ is supposed to be a $c$.

I will fix my original post right now, and thanks for catching that...:D
 

FAQ: Finding Triples to Satisfy $\frac{5}{2}$

What does it mean to find triples to satisfy $\frac{5}{2}$?

Finding triples to satisfy $\frac{5}{2}$ means finding three numbers that can be multiplied together to equal $\frac{5}{2}$. This is also known as finding a solution to the equation $xyz = \frac{5}{2}$.

Why is it important to find triples to satisfy $\frac{5}{2}$?

Finding triples to satisfy $\frac{5}{2}$ can be important in various mathematical and scientific applications. For example, in geometry, finding triples to satisfy $\frac{5}{2}$ can help in constructing right triangles with a specific ratio of side lengths. In physics, it can be used to solve for unknown variables in equations that involve $\frac{5}{2}$.

How do you find triples to satisfy $\frac{5}{2}$?

There are multiple ways to find triples to satisfy $\frac{5}{2}$. One approach is to use trial and error, plugging in different values for each variable until a solution is found. Another approach is to use algebraic manipulation, such as factoring or substitution, to solve for the variables.

Are there multiple sets of triples that can satisfy $\frac{5}{2}$?

Yes, there can be multiple sets of triples that can satisfy $\frac{5}{2}$. For example, if we let $x = 1$, then $y = 5$ and $z = \frac{1}{2}$ would satisfy the equation $xyz = \frac{5}{2}$. However, if we let $x = \frac{1}{2}$, then $y = 10$ and $z = \frac{1}{2}$ would also satisfy the equation. These are two different sets of triples that satisfy $\frac{5}{2}$.

Can triples be negative or fractions when solving for $\frac{5}{2}$?

Yes, triples can be negative or fractions when solving for $\frac{5}{2}$. For example, if we let $x = -2$, then $y = -\frac{5}{2}$ and $z = \frac{1}{2}$ would satisfy the equation $xyz = \frac{5}{2}$. This is a valid solution, as the product of these three numbers is still equal to $\frac{5}{2}$.

Similar threads

MHB New Year Challenge: Find Real Number Triples
Replies
1
Views
853
MHB Roots of Polynomial: Find $\frac{1}{A}+\frac{1}{B}+\frac{1}{C}$
Replies
1
Views
967
MHB How to Convert Miles to Kilometers with a Conversion Chain
Replies
6
Views
1K
MHB Find Product: $(a^4+b^4+c^4)$ and $(a^6+b^6+c^6)$
Replies
3
Views
973
MHB Find the amount of sand in each bag
Replies
1
Views
915
MHB Uncovering Overlooked Solutions: Solving a Triple Integer Equation
Replies
3
Views
2K
MHB Real Numbers $a,\,b,\,c$ Solving System of Equations
Replies
2
Views
1K
MHB Prove $\frac{1}{3}\le \frac{u}{v} \le \frac{1}{2}$ with Triangle Sides
Replies
4
Views
1K
MHB Can You Solve This Challenging Inequality Problem?
Replies
1
Views
1K
MHB Proving $(a)^\dfrac{1}{3}+(b)^\dfrac{1}{3}+(c)^\dfrac{1}{3}=0$
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top