Im unsure how to simplify to this point can someone explain?
#Quadratic problem
polar plover
Is the final part in completing the square form?
i've put it in completing the square form and its closer to the answer
where have i gone wrong because the parts outside the square do not equate
wide galleon
Im unsure how to simplify to this point can someone explain?
Try working x^2-19y^2=z into the second equation.
Hint: ||How do you get z^2 from z?||
dry flint
Not sure if this will help but x^2 - 19y^2 is the field norm of Z[sqrt(19)],i.e. Elements of the form x +ysqrt(19) where x, y integers
I. E. I. E. w*conj(w), where conj(w) is x - yswrt(19)
wide galleon
Not sure if this will help but x^2 - 19y^2 is the field norm of Z[sqrt(19)],i.e....
That wont help. This problem is a precalculus problem.
wide galleon
Was just wondering if there was a neat trick involving that lol
I mean, you can't get a neater trick than squaring both sides of the original equation.
wide galleon
Substitution for z will work too I suppose.
dry flint
Both sides
polar plover
I mean, you can't get a neater trick than squaring both sides of the original eq...
yep thats what i had done
i probably should've made that more clear
polar plover
im stuck at the point of the bottom equation
my steps so far were to square x² - 19y²
then expand that to x⁴ - 38x²y² + 361y⁴
from there I recognised that the answer equation is in the form (ax² + b)² + c and thats similar to the (ax + b)² + c form of completing the square
im not quite sure how to complete the square on polynomials larger than 2
idle rockBOT
Solved