- #1

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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) ?

- Thread starter issac newton
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- #1

- 14

- 0

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) ?

- #2

- 45

- 0

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

- #3

- 14

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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 ??

- #4

- 34,627

- 6,003

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

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 ??

- #5

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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 ??

- #6

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

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.

- #7

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thank u abacus.

i think the answer is 22 and 3.

22*3=66

22-3=19

22+3=25

i think the answer is 22 and 3.

22*3=66

22-3=19

22+3=25

- #8

- 34,627

- 6,003

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.

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