How to solve the equation of $\sqrt{x}+\sqrt{y}=\sqrt{2205}$ in integers? How in general to solve the similar equations?
2026-04-08 01:16:05.1775610965
How to solve the equation of $\sqrt{x}+\sqrt{y}=\sqrt{2205}$ in integers?
143 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in COMBINATORICS
- Using only the digits 2,3,9, how many six-digit numbers can be formed which are divisible by 6?
- The function $f(x)=$ ${b^mx^m}\over(1-bx)^{m+1}$ is a generating function of the sequence $\{a_n\}$. Find the coefficient of $x^n$
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Hard combinatorial identity: $\sum_{l=0}^p(-1)^l\binom{2l}{l}\binom{k}{p-l}\binom{2k+2l-2p}{k+l-p}^{-1}=4^p\binom{k-1}{p}\binom{2k}{k}^{-1}$
- Algebraic step including finite sum and binomial coefficient
- nth letter of lexicographically ordered substrings
- Count of possible money splits
- Covering vector space over finite field by subspaces
- A certain partition of 28
- Counting argument proof or inductive proof of $F_1 {n \choose1}+...+F_n {n \choose n} = F_{2n}$ where $F_i$ are Fibonacci
Related Questions in DIOPHANTINE-EQUATIONS
- Can we find $n$ Pythagorean triples with a common leg for any $n$?
- Can we find integers $x$ and $y$ such that $f,g,h$ are strictely positive integers
- Count of possible money splits
- I'm having a problem interpreting and starting this problem with primes.
- Solution of $X^5=5 Y (Y+1)+1$ in integers.
- Solving for 4 variables using only 2 equations
- Algorithm for diophantine equation
- Find all pairs of integers (x,y) such that $x(x+1)(x^2+x+2)=2y^2$
- Sum Equals Product: A Diophantine Equation
- Diophantine equation for Multivariate Polynomial
Related Questions in RADICALS
- Tan of difference of two angles given as sum of sines and cosines
- Symmetric polynomial written in elementary polynomials
- Interesting inequalities
- Prove that $\frac{1}{\sqrt{ab+a+2}}+ \frac{1}{\sqrt{bc+b+2}}+ \frac{1}{\sqrt{ac+c+2}} \leq \frac{3}{2}$
- Radical of Der(L) where L is a Lie Algebra
- Find local extrema $f(x_1,x_2, \ldots , x_n) = \sqrt{(x_1+x_2+\ldots x_n-a)(a-x_1)(a-x_2)\cdots (a-x_n)}$
- A non-geometrical approach to this surds question
- If $\sqrt{9−8\cos 40^{\circ}} = a +b\sec 40^{\circ}$, then what is $|a+b|$?
- Finding minimum value of $\sqrt{x^2+y^2}$
- Polynomial Equation Problem with Complex Roots
Related Questions in INTEGERS
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Which sets of base 10 digits have the property that, for every $n$, there is a $n$-digit number made up of these digits that is divisible by $5^n$?
- Ring of remainders definition
- Proof of well-ordering property
- Compute a division with integer and fractional part
- Solving for 4 variables using only 2 equations
- For any natural numbers a, b, c, d if a*b = c*d is it possible that a + b + c + d is prime number
- Can I say this :$e^{{(294204)}^{1/11}}-{(294204)}^{1/11}$ integer number or almost integer?
- Pack two fractional values into a single integer while preserving a total order
- What will be the difference?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Simple factorization yields $\sqrt{2205} = 21\sqrt{5} $ $$\sqrt{x}=\sqrt{2205}-\sqrt{y}$$ $$x=2205+y-2.21\sqrt{5}\sqrt{y}$$ $$42\sqrt{5y}=2205+y-x$$ $$y\text{ is in the form of } 5k^2$$ $$y=k\sqrt{5}\Rightarrow\sqrt{x}=l{5}$$
Then we have,
$\sqrt{x}=0,\sqrt{y}=21\sqrt{5}$
$\sqrt{x}=\sqrt{5},\sqrt{y}=20\sqrt{5}$ and so on...
For these type of problems, use the fact that $a+\sqrt{b}=c+\sqrt{d}$ where b,d are not perfect squares $\Rightarrow a=c \text{ and } b=d$