I tried equating the phytagoras and quadratic formula
#why can't wolfram solve this
foggy moth
analog isleBOT
foggy moth
Im just trying to see the values of a b and c where both the quadratic formula and phytagoras therom are equal to 0
@velvet steeple
velvet steeple
Ok, so Wolfram still wouldn't be able to solve that
foggy moth
How do I solve it
velvet steeple
There is no one answer
Which is why it can't solve it
There are an infinite number of answers
velvet steeple
What do you mean real solutions?
Real solutions would mean that b^2-4ac > 0
These formulas are too complicated to try to solve
random crane
you're trying to solve for 3 unknowns with 1 equation
velvet island
given that a, b, c are part of the real numbers set, there are an infinite amount of solutions (more specifically, the real numbers set includes numbers from {x | -∞ < x <∞} so there are infinite solutions for the equation)
foggy moth
Real solutions would mean that b^2-4ac > 0
So b^2-4ac is greater and equal to a^2+b^2-c^2
Because a^2+b^2-c^2=0
@velvet island
velvet island
So b^2-4ac is greater and equal to a^2+b^2-c^2
given that b^2-4ac > 0 that would imply that b^2-4ac will always be positive but we're trying to compare two different equations meant for two different purposes
foggy moth
We're trying to find the values of a b and c where a^2+b^2-c^2=the quadratic fromula
velvet island
didn't you say the values were 0 somewhere or am i going insane? 😓
i mean i can do a proof by induction tomorrow and see how that comes out?
for when a, b, c = 0 it's true
foggy moth
Technically
A b c don't all have to be 0
And you can't divide with 0 so a ≠0
So two values
Have to be the same
C^2 has to be anything but 0
So that a^2-c^2=0
velvet island
i swear somewhere someone said that we set a b and c to 0 😭
foggy moth
If a^2=c^2 then b has to be 0
So a=1
C=1
and b=0 or am I wrong
Because 1 is the only value bigger than 0 where they are equal it can also be -1
Wait actually
b=0
And a and c are everything but 0
But a must =c
velvet island
well traditional pythag states that c = sqrt(a^2 + b^2) so given those values:
foggy moth
So that's true
But what about a=1 and c=1 and b=0 in the quadratic formula
It would translate to 0±square root of -4ac/2a
velvet island
well quadratic formula produces two solutions which are the roots of said parabola
foggy moth
Ye because we know x=0
For quadratic
So it would mean
1 is wrong
Because that doesn't give the value of zero when subbed into the quadratic formula
velvet island
foggy moth
So for this to be true b must =0 c must =0 but a≠0
foggy moth
We're trying to find the values of a b and c where a^2+b^2-c^2=the quadratic fro...
So it has to be a non real solution
For a
Or
velvet island
Let's see -1 then
foggy moth
Or a=-b where b=-a
And c=0
@velvet island
Look here's a vase it works in
Wait
What if
foggy moth
Wait
It has to be-(-1)
But the problem is its not true for both cases of the quadratic formula
So we need to find a case for a b and c to be equal for both cases of the quadratic formula
@velvet island
Is that possible
plush scarab
[a,b,c] = [-1, -1, 2]
[a,b,c] = [1, 1, -2]
more answers probably exist
foggy moth
Do they work if you plus or add in the quadratic formula
plush scarab
one is plus, one is minus
foggy moth
[a,b,c] = [-1, -1, 2]
[a,b,c] = [1, 1, -2]
more answers probably exist
You mean these are the first values which are correct
Oh ok
That we have found
plush scarab
[a,b,c] = [+-sqrt(1/2), -a, 0]
foggy moth
[a,b,c] = [+-sqrt(1/2), -a, 0]
Another solution?
foggy moth
[a,b,c] = [-1, -1, 2]
[a,b,c] = [1, 1, -2]
more answers probably exist
Which solutions are the plus in ± and which are the - in ±
foggy moth
Which solutions are the plus in ± and which are the - in ±
Then how is -1 here =a
Is it because c≠0