# 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 ??

Homework Helper
Gold Member
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