scoatem y din a 2a:
2y^2+3xy+1=0
delta=9x^2-4*2*1=9x^2-8
y1= [tex] \frac{-3x+ \sqrt{9x^2-8} }{4} [/tex]
y2=[tex] \frac{-3x- \sqrt{9x^2-8} }{4} [/tex]
scoatem y din prima :
y=[tex] \frac{-8+x^2}{7x} [/tex]
egalam y1 cu y si aflam x-urile:
[tex] \frac{-3x+ \sqrt{9x^2-8} }{4} [/tex] = [tex] \frac{-8+x^2}{7x} [/tex]
cativa pasi de aranjare:
[tex]-3x+ \sqrt{9x^2-8}= \frac{-32+4x^2}{7x} [/tex]
[tex]-21x^2+7x \sqrt{9x^2-8}=-32+4x^2 [/tex]
[tex]-25x^2+32=-7x \sqrt{9x^2-8} [/tex]
ridicam la patrat
[tex]625x^4+32*32-2*32*25*x^2=49x^2*9x^2-49x^2*8[/tex]
[tex]184x^4-1208x^2+1024=0[/tex]
notam x^2=t
[tex]184t^2-1208t+1024=0[/tex]
rezolvam ec. cu delta
delta=705600
=> radical din delta = 840
