1
a) x=-√2
b) x=0,16/8=0,02
c) x=√6
2
a) sin 30⁰=cos 60⁰ =1/2
b) x=3
(m-1)x=12
m-1=4
m=5
c) 12+8+20=40
8+20=28
probabilitatea ca bila sa nu fie alba este de 28/40
3.
a) h=√5x20=√100=10 cm
b) diagonala=√(10²+10²)=10√2
c) sin(< B)=2/3
sin (<B) =AC/AB
AC=2
AB=3
CB=√(3²-2²)=√--4=√5
AB/BC=2/√5
4.
a) 2n+n/4=n+25
8n+n=4n+100
5n=100
n=20
b) x=cateta
x+3=ipotenuza
x²+x²=2x²
x√2=x+3
x√2-x=3
x(√2-1)=3
x=3/(√2-1) =3(√2+1)/(√2-1) (√2+1)=3(√2+1)
P=3(√2+1)+3(√2+1) +3(√2+1) +3=9(√2+1)+3
5.
(x+3)²+2(x-4)(x+3)+(x-4)² =
=x²+6x+9+2(x²-4x+3x-12)+x²-8x+16=
=x²+6x+9+2x²-8x+6x-24+x²-8x+16=
=4x²-4x+1=(2x-1)²
(2x-1)² ≥0
deoarece patrat perfect
E(x)=1
(2x-1)²=1
2x-1=1 ⇒ x=1
2x-1=-1 ⇒ x=0
