Possible values of X and Y for the problem

[issac newton]

X and Y are whole nos
X+Y= square of a no.
X-Y=prime no.
X*Y=twin no. (eg 77)
X/Y=irrational no.

how to solve such kind of problems apart from trial n error basis(ad hoc) ?

 

[acabus]

If x and y are whole numbers, then x/y can't be irrational.

 

[issac newton]

sorry abt the fourth condition. what if first 3 conditions are considered ??

X+Y= square of a no.
X-Y=prime no.
X*Y=twin no. (eg 77)

what are the possible values of x and y. how to approach such a problem to narrow down our answers ??

 

[haruspex]

sorry abt the fourth condition. what if first 3 conditions are considered ??

X+Y= square of a no.
X-Y=prime no.
X*Y=twin no. (eg 77)

what are the possible values of x and y. how to approach such a problem to narrow down our answers ??

Start with the last condition. What does that allow you to say about X and Y? (either one of them is 1 or ...?)

 

[issac newton]

The value of x or y can be 1 or 11. but all values of x with y being 1,will not satisfy the other two conditions. like
99*1=99 but

99-1=98 not a prime.

so i considered y=11, thus x+y should b greater than 11 n a square no: so it starts from 16(x+y) and goes on... but this method is ad hoc n i did not get any solution for this because 1 condition always fails for some x value.

is there any equation solving method and also can this question have a solution if at all ??

 

[acabus]

The value of x or y can be 1 or 11. but all values of x with y being 1, will not satisfy the other two conditions. like
99*1=99 but

99-1=98 not a prime.

so i considered y=11, thus x+y should b greater than 11 n a square no: so it starts from 16(x+y) and goes on... but this method is ad hoc n i did not get any solution for this because 1 condition always fails for some x value.

is there any equation solving method and also can this question have a solution if at all ??

99 = 3 * 33, so 1 and 11 aren't the only values x or y can take.

There's 1 solution to your problem.

Don't be surprised that you're getting "ad hoc" methods, you've thrown together a few random arbitrary conditions, especially the "twin number" bit.

 

[issac newton]

thank u abacus.

i think the answer is 22 and 3.

22*3=66

22-3=19

22+3=25

 

[haruspex]

Ok, I misunderstood. I thought by "twin" number you meant a semiprime. You just mean two digits the same, right?
Typically there are no equations for these sorts of problems. The technique is to start with the pieces of information that narrow down the possibilities fastest.
Btw, for X*Y there are also possibilities like 3*22, etc.