Well i hope you guys had a nice break and some good rest because the madness is starting again :D . This lesson we started with Mr Piateks New Years story which was dealing with stucking in Fargo but i guess he had some nice time at the mall. Ok Lets go to the topic we basically catched up where we stopped before the break so yeah here you go :
we were talking about Quadratic-quadratic system :
there are either 0,1,2,3 or 4 solutions
today we did two examples one with supstitution and the other one with elimination :
1 Supstitution :
x² - y² = 5
xy + 6 = 0 -> y = -6/x
x² - (-6/x)² = 5
x^4- 36/x² = 5
x^4 -5x² - 36 = 0
(x² -9) (x² +4) = 0
x² -9 = 0 or x² + 4 = 0
x² = 9 x² = -4
x = +/- Sqaureroot 9
x = +/- 3
Final solutions ( 3,-2) (-3,2)
now by Elemination :
x² +4y² = 49
2x² - 3y² = -12
2x² + 8y² = 98
2y² -3y² = -12
11y² = 110
y² = 10
y = +/- sqaure root10
x² + 4y² = 49
x² + 4 (Sqiare root 10) ² = 49
x² = 49-40
x² = 9
x = +/- 3
final solutions : (3,squarer. 10) ( 3, - squarer. 10) ( -3. sqaurer. 10) ( -3,-squarer. 10 )
K i hope you guys got it a little bit more :) night
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