HELPPPPPP i wanna solve this but without squaring both sides (using a clever trick)
ig imon the right ath but dont seem to find the right answer, enter the thread to see my though process
#ALgebra
fiery nest
azure nymphBOT
HELPPPPPP i wanna solve this but without squaring both sides (using a clever tri...
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tawdry remnant
i mean 69 + 6 =/= 71
tawdry remnant
doing it by squaring both sides is also not that bad
tawdry remnant
hefty long solution
ehh
tawdry remnant
yeah you get the same quadratic, -x^2 + 138x - 4761, the other way
so, conveniently, 138^2 = 4*4761
so the discriminant is 0
however good luck working that out
fiery nest
i dont like substituting y+x^2 type
my purpose was an aproach different than normal one
after all im giving the second toughest exam
anyways thank you
: D
fiery nest
was this a real question from a test
dpp
tawdry remnant
i wonder if there is some very slick number theory way if you assume the answer is an integer
fiery nest
number theory scares me 💀
tawdry remnant
we need a^2 | x + 36, b^2 | (2x-33)
actually
x + 36 = na^2, 2x-33 = nb^2, 6x+6 = n(a+b)^2
n,b both odd, so a is also odd, so x is odd
fiery nest
lemme make this out
if x+36 = na^2
wouldnt 2x-33 = mb^2?
howd we know its the same factor for both (n)
tawdry remnant
the power of intuition
nah im not sure but i think if that is true it should be figureoutablewhy
fiery nest
we cant just assume it like that?
tawdry remnant
we cant just assume x is an integer either
fiery nest
did we?
tawdry remnant
i wonder if there is some very slick number theory way if you assume the answer ...
.
fiery nest
my bad
fiery nest
we need a^2 | x + 36, b^2 | (2x-33)
actually
x + 36 = na^2, 2x-33 = nb^2, 6x+6 =...
shouldnt this work even when x is not an integer
tawdry remnant
| is only defined for integers, as is evenness/oddness
some stuff may still be workable if you only assume x is rational
fiery nest
ouh we studied this as if x|y x is divisible by y (x/y = integer)
doesnt matter if x and y are integers or not
tawdry remnant
thats a possibility
fiery nest
yeah its what im talking about
sick shore
andy math ?
fiery nest
i aint watching his solution 💀
i was just working out for some unique trick workeable on any question im stuck on
just boosting my solving capabilities
tawdry remnant
n,x are both 1 mod 4
3x = -1 mod 16 (from last equation, n == 1 mod 4, (a+b)^2 == 4 mod 4)
x = 5 mod 16
na^2 = nb^2 = 9 mod 16
so a = b or a = -b mod 16
sick shore
is mod the same thing as it is in programming
fiery nest
remainder thing
sick shore
yea thats it
echo plinth
is mod the same thing as it is in programming
yeah pretty much
tawdry remnant
however if 16 | (a+b) then the lhs is a multiple of 256
meanwhile, 6x + 6 = 6(4k + 2) = 12(2x + 1)
which is not a multiple of 256
so a == b mod 16
anyway, at this point i think this is harder than the normal method(s), but you can try doing it this way kind of like a puzzle
fiery nest
+close