Question

(10x+y)*(10y+x)=2430

Answer 1

 2430=2*3^5*5 
 Если  
 {10x+y=a 
 {10y+x=b 
  
 9(y-x)=b-a  
 то есть b-a, должна быть кратна 9. 
 так как  a,b это сочетание каких то чисел 2,3^5,5  то решение имеется,   тогда когда 
 1)a=3^k*5, b=3^(5-k)*2  
 2)a=3^k*2, b=3^(5-k)*5   
 
 {10x+y=3^2*5 
 {10y+x=3^3*2   
  
 {10x+y=3^3*2 
 {10y+x=3^2*5   
 
 {10x+y=-3^2*5 
 {10y+x=-3^3*2 
 
 {10x+y=-3^3*2 
 {10y+x=-3^2*5 
 
 откуда (4,5) (5,4) (-4,-5) (-5,-4)  

Answer 2

To solve the equation (10x + y) * (10y + x) = 2430, we need to find the values of x and y that satisfy the equation.

Let's expand the equation and simplify it:

(10x + y) * (10y + x) = 2430 10x * 10y + 10x * x + y * 10y + y * x = 2430 100xy + 10x^2 + 10y^2 + xy = 2430 101xy + 10x^2 + 10y^2 = 2430

Now, since 2430 is not a large number, we can try different combinations of x and y to see if any of them satisfy the equation.

Let's start with xy = 1:

101 * 1 + 10 * 1^2 + 10 * 1^2 = 101 + 10 + 10 = 121 (which is not equal to 2430)

Now, let's try xy = 2:

101 * 2 + 10 * 2^2 + 10 * 2^2 = 202 + 40 + 40 = 282 (which is not equal to 2430)

Next, let's try xy = 3:

101 * 3 + 10 * 3^2 + 10 * 3^2 = 303 + 90 + 90 = 483 (which is not equal to 2430)

We can keep trying different values of xy, but as we can see, none of the combinations yield 2430.

It's important to note that there may be some other values of x and y that satisfy the equation, but they might be more difficult to find manually. In such cases, numerical methods or algebraic techniques might be used to find solutions. If you are looking for specific solutions, please let me know, and I can assist you further.