Solving for $k$: $k^2=x+y$ and $k^3=x^2+y^2$

  • MHB
  • Thread starter anemone
  • Start date
In summary, the equation for solving for k is k^2=x+y and k^3=x^2+y^2. It is important to solve for k in order to find the value of the unknown variable and better understand the relationship between x and y. The process for solving for k involves algebraic manipulation and substitution, potentially using square roots or cubed roots. The potential solutions for k can vary and it is important to check for extraneous solutions. Solving for k can have applications in real-world situations, such as mathematical modeling and problem-solving.
  • #1
anemone
Gold Member
MHB
POTW Director
3,883
115
Find all non-negative integers $k$ such that there are integers $x$ and $y$ with the property

$k^2=x+y$ and $k^3=x^2+y^2$
 
Mathematics news on Phys.org
  • #2
Hint:

Compare $2(x^2+y^2)$ and $(x+y)^2$.
 

FAQ: Solving for $k$: $k^2=x+y$ and $k^3=x^2+y^2$

What is the equation for solving for k?

The equation for solving for k in this scenario is k^2=x+y and k^3=x^2+y^2.

Why is it important to solve for k in this equation?

Solving for k allows us to find the value of the unknown variable in the equation, which can help us better understand the relationship between x and y in the given scenario.

What is the process for solving for k in this equation?

The process for solving for k involves using algebraic manipulation and substitution to isolate k on one side of the equation and solve for its value. This may involve taking square roots or cubed roots, depending on the given equation.

What are the potential solutions for k in this equation?

The potential solutions for k can vary depending on the given values of x and y. In some cases, there may be multiple solutions or no real solutions at all. It is important to check for extraneous solutions when solving for k.

How can solving for k help us in real-world applications?

Solving for k can help us understand and predict relationships between variables in real-world situations, such as in mathematical modeling or scientific experiments. It can also help us solve practical problems, such as finding the missing side length of a triangle in geometry.

Similar threads

Exploring an Unexplored Expression for the Beta Function
Replies
2
Views
1K
I Partial Differential Equation solved using Products
Replies
2
Views
1K
MHB Finding $k$ for 2 Non-Negative Roots of $x^2-2x\lfloor x \rfloor +x-k=0$
Replies
2
Views
1K
MHB Prove Divisibility: $(x-y)^2+(y-z)^2+(z-x)^2=xyz$ yields $x^3+y^3+z^3$
Replies
1
Views
1K
MHB What are the values of n and k in n+8=2^k when n!+8 = 2^k?
Replies
8
Views
1K
MHB Find the possible values of k: x+1/y=y+1/z=z+1/x=k
Replies
2
Views
2K
MHB 6.2.8 {{k,4},{3,k}}=k what is k
Replies
3
Views
1K
MHB Factorize 6(x^5+y^5+z^5)-5(x^2+y^2+z^2)(x^3+y^3+z^3)
Replies
1
Views
942
MHB :Calculating $k$ to Find Wire Length
Replies
5
Views
1K
MHB Positive Integer Solutions of $(x^2+y^2)^n=(xy)^{2014}$
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top