Question

Exercitiile urmàtoare 2/3

Answer 1

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

$ON=\frac{AO\times OB}{AB}=\frac{2\times6}{2\sqrt{10} } =\frac{3\sqrt{10} }{5}$

ON║PF⇒

$\frac{BO}{BP} =\frac{ON}{PF} \\\\\frac{6}{8}=\frac{\frac{3\sqrt{10} }{5} }{PF}$

$PF=\frac{\frac{24\sqrt{10} }{5} }{6} =\frac{4\sqrt{10} }{5}$