Question

Rozwiąż równanie kwadratowe

a) 3/4y2+9=y/2+(y-3)2

b) 4/3y2=3/4y+1/4y2

Answer 1

a) ¾y²+9=y/2+(y-3)²

¾y²+9=y/2 + y²-6y+9 .... /-9

¾y²-y²-y/2+6y=0 .... /*2

1,5y²-2y²-y+12y=0

-½y²+11y=0

y(-½y+11)=0

y=0 ∨ -½y+11=0

y=0 ∨ ½y=11

y=0 ∨ y=22

 

b) 4/3y²=3/4y+1/4y²

4/3y²-1/4y²-3/4y=0

16/12y²-3/12y²-3/4y=0

13/12y²-9/12y=0

y(13/12y-9/12)=0

y=0 ∨ 13/12y-9/12=0

y=0 ∨ 13/12y=9/12

y=0 ∨ y=9/12 * 12/13

y=0 ∨ y=9/13