2.
E(x)=(x²-2x+3)²-(x²-2x)²-2x(3x-7)-5
a.
E(x)=x⁴+4x²+9-4x³-12x+6x²-x⁴+4x³-4x²-6x²+14x-5
E(x)=9-12x+14x-5=2x+4
b.
E(n)=2n+4
2n+4<12
2n<8
n<4
n={1,2,3}
3.
f(x)=-3x+6
a)
∩OX
y=0
-3x+6=0
x=2
A(2,0)
∩OY, x=0
y=0+6=6
B(0,6)
b.
In ΔAOB aplicam Pitagora
AB²=AO²+OB²
AB²=36+4=40
AB=2√10
Fie PF⊥AB
d(P,AB)=PF
Fie ON⊥AB
ON║PF
ON este inaltime in ΔAOB dr in O
[tex]ON=\frac{AO\times OB}{AB}=\frac{2\times6}{2\sqrt{10} } =\frac{3\sqrt{10} }{5}[/tex]
ON║PF⇒
[tex]\frac{BO}{BP} =\frac{ON}{PF} \\\\\frac{6}{8}=\frac{\frac{3\sqrt{10} }{5} }{PF}[/tex]
[tex]PF=\frac{\frac{24\sqrt{10} }{5} }{6} =\frac{4\sqrt{10} }{5}[/tex]
