Question

Rezolvati in R ecuatia:
2(x-1)²=3x+2
(x-2)(x+3)=24
(x-3)(x+2)=14
URGENT

Answer 1

Prima: 2(x la a 2-2•-1•x+-1 la 2)=3x+2
2(x la a 2 +x+1)=3x+2
2x la 2 +2x+2=3x+2
2x la 2+2x+2-3x-2=0
2x la 2-x=0
x(2x-1)=0=>x=0 si 2x-1=0
2x=1
x=1/2

A doua : (x-2)(x+3)=24
x•x+3x-2x-6=24
x2+x-6=24
x2+x-6-24=0
x2+x-30=0
∆=b2-4ac
= 1 la a 2-4•1•(-30)
=1+120
=121
x1,2=-b+-√∆/2a
=-1+-11/2
x1=-1-11/2=-12/2=-6
x2=-1+11/2=10/2=5

A treia: (x-3)(x+2)=14
x2+2x-3x-6=14
x2-x-6-14=0
x2-x-20=0
∆=b2-4ac
=(-1) la 2 - 4•1•-20
=1+80=81

x1,2=-b+-√∆/2a
=1+-√81/2
x1=1+9/2=10/2=5
x2=1-9/2=-8/2=-4