Question

1. Rozwiąz równianie:
a. x+7 / x-4 + x-7/ x-2 = 22 / x(do kwadratu) -6x +8

2. Które wyrazy ciągu an sa dodatnie
a. an= 10- 3n
b. an- 2n do kwadratu +n - 6

Answer 1

Zad 1.
a)x+7/x-4+x-7/x-2=22/x (do kwadratu)-6x+8
(x+7)(x-2)/(x-4)(x-2)+(x-7)(x-4)/(x-4)(x-2)=22*(x-4)(x-2)/(x do kwadratu -6x+8)(x-4)(x-2)
x do kwadratu -2x+7x-14/(x-4)(x-2)+ x do kwadratu -4x-7x+28/(x-4)(x-2)=(22x-88)(x-2)/(x-4)(x-2)
x do kwadratu +5x-14/(x-4)(x-2)+x do kwadratu-11x+28/(x-4)(x-2)=22x do kwadratu-44x-88x+176/(x-4)(x-2)
(x-2)(x+7)/(x-4)(x-2)+(x-4)(x-7)/(x-4)(x-2)=22x do kwadratu-132x+176/(x-4)(x-2)(x+7)/(x-4)+(x-7)/(x-2)=(11x-44)(2x-4)/(x-4)(x-2)
(x+7/(x-4)+(x-7)/(x-2)=(pierwiastek z 11x-pierwiastek z 44)(pierwiastek z 11x+pierwiastek z 44)/(x-4)(x-2)

Zad 2.
a) a(0)=10-3*0=10-0=10 
a(1)=10-3*1=10-3=8          
a(2)=10-3*2=10-6=4           
a(3)=10-3*3=10-9=1         
b) a(2)-2*2(do kwadratu)+2-6    a(3)-2*3(do kwadratu)+3-6  a(4)-2*4(do kwadratu)+4-6
    a(2)-2*4+(-4)                       a(3)-2*9+(-3)                     a(4)-2*16+4-6
    a(2)-8+(-4)                          a(3)-18+(-3)                      a(4)-32+(-2)
    a(2)=8+(-4)                         a(3)=18+(-3)                     a(4)=32+(-2)
    a(2)=4                                a(3)=15.                           a(4)=30 itd.