Question

1.Sa se rezolve ecualtiile:(toate)
a)(x-1)²=9
b)3-(x-5)²=1
c)(3-x)(3+x)-6=2
d)5-(x-2)(x+2)=3
e)x²-2x+1=7
f)4x²-4+1=5


2.Descompuneti in factori:
a) x²-5x*6=
b)x²-5x+6=
c)x²-7x*10=
d)x²-10x*24=

Answer 1

a)(x-1)²=9
(x-1)²=3²
x-1=3
x=4

b)3-(x-5)²=1
3-1=(x-5)²
(x-5)² = 2
x-5=√2
x=√2+5

c)(3-x)(3+x)-6=2
9-x²-6=2
9-6-2=x²
x²=1
x=1

d)5-(x-2)(x+2)=3
5-(x²-4)=3
x²-4=2
x²=6
x=√6

e)x²-2x+1=7
(x-1)²=7
x-1=√7
x=√7+1

f)4x²-4+1=5
4x²=5+4-1
4x²=8
x²=2
x=√2

2.Descompuneti in factori:
a) x²-5x*6=x(x-30) 
b)x²-5x+6= x²-3x-2x+6=x(x-3)-2(x-3)=(x-3)(x-2)
c)x²-7x*10= x(x-70)
d)x²-10x*24=x(x-240)