It looks symmetrical. Suppose x=y and equation 1 becomes 1/2 + 1/2 = 1 then 16^(x²+x)=1/2 or 2^(4(x²+x))=2^-1 or 4(x²+x)=-1 or 4x²+4x+1=0 giving x=-0.5=y as a solution.
Assumption x=y because of the symmetry only is not legal in general case. Just a simple example: x+y=1. Symmetrical? Yes. But x=y substitution doesn't give us all the possible solutions. Symmetry itself does not determine the equality of x and y. It determins only that each solution have a symmetric pair. Such as (1,0) and (0,1) in my example. So in your case you should've proven there's no solutions for x not equal to y.
if (x1,y1) be the solution of this eqn then (y1,x1 ) will also be the solution of this and its only possible if (x1,y1) lies of the line Y= X so putting y =x in eq we get 2*16^(x+ x^2) =1 16^(x+ x^2) = 1/2 = 16^(-1/4) x^2+x-1/4 = 0 x = -1/2
@@armansimonyan5772 yes you are right line y = x is just a subset of the solution The correct conclusion will be as if an equation is symmetrical ( means if you interchange x with y the equation remains same ) Then for every sol (a,b) there exists a solution (b,a) and if we mark these coordinates on Cartesian plane than (a,b) and (b,a) would be at same distance from line y = x And yes my way of solving and getting correct answer was maybe just a coincidence not very sure about it
Beautiful ❤😊
Thank you! 😊🥰
It looks symmetrical. Suppose x=y and equation 1 becomes 1/2 + 1/2 = 1 then 16^(x²+x)=1/2 or 2^(4(x²+x))=2^-1 or 4(x²+x)=-1 or 4x²+4x+1=0 giving x=-0.5=y as a solution.
You could have said "It is symmetrical" instead of "It looks symmetrical".
Assumption x=y because of the symmetry only is not legal in general case.
Just a simple example: x+y=1.
Symmetrical? Yes.
But x=y substitution doesn't give us all the possible solutions.
Symmetry itself does not determine the equality of x and y. It determins only that each solution have a symmetric pair. Such as (1,0) and (0,1) in my example.
So in your case you should've proven there's no solutions for x not equal to y.
How in the world did you set them eqaul to 0 at the end? I thought it must be a product. Or is there some rule I do not know about
Sum = 0 , squares must be 0 .
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5:54 Loved the insane step. I actually predicted it would happen right there. You know pretty well I watch just for that. Very "good".
6:46 oooh you decided to NOT go with the log ... Hahahahahahaha. Amazing. That's even best. You are the second best fake Math content creator.
The answer is not unique for an equation with two unknowns.
if (x1,y1) be the solution of this eqn then (y1,x1 ) will also be the solution of this and its only possible if (x1,y1) lies of the line Y= X
so putting y =x in eq we get 2*16^(x+ x^2) =1
16^(x+ x^2) = 1/2 = 16^(-1/4)
x^2+x-1/4 = 0
x = -1/2
Why is it only possible if x=y? The conclusion appears to be right but I do not think the reasoning is.
@@armansimonyan5772 yes you are right line y = x is just a subset of the solution
The correct conclusion will be as if an equation is symmetrical ( means if you interchange x with y the equation remains same )
Then for every sol (a,b) there exists a solution (b,a) and if we mark these coordinates on Cartesian plane than (a,b) and (b,a) would be at same distance from line y = x
And yes my way of solving and getting correct answer was maybe just a coincidence not very sure about it