Question

Dau 99 de puncte!!!!!!!Mariangel ma ajuti?
1. Sa se calculeze media aritmetica si media geometrica a numerelor:
a=5+2√6
b=5-2√6
2.Efectuati :
(7+4√3)(7-4√3)=?
3.Calculati:
$25x^n +5x^{n+2}$
4.Descompuneti in factori:
$a)x^3-x^2-x+1$
$b)x^3+6x^{2y}+9xy^2$.

Answer 1

1.Ma=(5+2√6+5-2√6)/2=10/2=5                             formula:
Mg=√(5+2√6)(5-2√6)=√(25-24)=√1=1                 (a+b)(a-b)=a↑2-b↑2
                                                                      
2.49-48=1

3.5↑2x↑n+5x↑n*x↑2=5x↑n(5+x↑2)

4.a)x(x↑2-x-1)+1
  b)x(x↑2+6x la 2y-1 +9y↑2)

Answer 2

1.media aritmetica:
$\frac{</span><span>5+2[tex] \sqrt{6}$+5-2$\sqrt{6}$}{2} = \frac{10}{2} [/tex]=5 
media geometrica:                      
$\sqrt{(5+2 \sqrt{6} )(5-2 \sqrt{6} )}$=$\sqrt{25-24}$=1 
Am folosit formula:
(x+y)(x-y)=$x^{2} - y^{2}$
                                                                      
2. Folosim aceeasi formula de mai sus:
(7+4√3)(7-4√3)=49-48=1

3. $25 x^{n} +5 x^{n+2}$=
=5*5$x^{n}$+5*$x^{n} * x^{2}$=
=$5 x^{n}$(5+$x^{2}$)

4.a) $x^{3} - x^{2} -x+1$=
=$x^{2} (x-1)-(x-1)$=
=(x-1)($x^{2} -1$)=
=(x-1)(x-1)(x+1)=
=(x+1)$(x-1)^{2}$

  b) $x^{3} +6 x^{2} y+9x y^{2}$=
=x($x^{2} +2*x*3y+ (3y)^{2}$)=
=x$(x+3y)^{2}$