>The problem does not state that the numbers have to be integers. a and b happen to be 9 +- 2 sqrt(11)
but the problem does state that you should be able to do it in your head. who exactly should be able to formulate and reduce simultaneous equations in xy then apply the quadratic formula (with some spicy +/- to keep track of) to get an answer with an irrational number, all in their head? usually, when a problem like this is given there is a shortcut that leads to a simple, not only rational but integer, answer.
the statement "you can do it in your head" generally does not entail this much complexity, as the person who said "you can do it in your head" comes out and says after previously spending a fair amount of time working on it.
words matter, people, that's why I didn't throw in the adjective integral even though I could have.
> the statement "you can do it in your head" generally does not entail this much complexity
It's funny that you jump to accusing OP of falsely claiming you can do it in your head, without apparently considering the alternative: that the intended solution is a simpler one than you outlined.
Trust me, you can do this in your head if you know basic high school level math, and you don't need to solve quadratic equations or keep a ton of numbers in your head at the same time.
If I ask you if 123456789 is a prime number, do you complain that it's not fair to make you perform division on such a long number?
fsckboy|3 months ago
but the problem does state that you should be able to do it in your head. who exactly should be able to formulate and reduce simultaneous equations in xy then apply the quadratic formula (with some spicy +/- to keep track of) to get an answer with an irrational number, all in their head? usually, when a problem like this is given there is a shortcut that leads to a simple, not only rational but integer, answer.
the statement "you can do it in your head" generally does not entail this much complexity, as the person who said "you can do it in your head" comes out and says after previously spending a fair amount of time working on it.
words matter, people, that's why I didn't throw in the adjective integral even though I could have.
forbiddenvoid|3 months ago
IanCal|3 months ago
If you have a+b and a-b you’ll get 2a when added together.
So knowing just the sum we can say that a is 9 in this setup.
Now we need to figure out b.
Multiplying out those you get
a^2 + ab -ab - b^2
And I get a longing for not having started this a phone.
Cancels and fill in what we know and we get 81 - b^2 = 37
b = sqrt(44) = sqrt(4)*sqrt(11) = 2sqrt(11)
sltkr|3 months ago
It's funny that you jump to accusing OP of falsely claiming you can do it in your head, without apparently considering the alternative: that the intended solution is a simpler one than you outlined.
Trust me, you can do this in your head if you know basic high school level math, and you don't need to solve quadratic equations or keep a ton of numbers in your head at the same time.
If I ask you if 123456789 is a prime number, do you complain that it's not fair to make you perform division on such a long number?
jhncls|3 months ago
pretzellogician|3 months ago