Question

1. wykonaj dzialania i doprowadz do najprostszej postaci
(a-3b)²-2(a+b)(3a-b)-6b²=
(a-b)²-(3a+2b)(3b-2a)=
(a-4b)²-(3a+b)(b-2a)=
(2a+b)²-2(a-b)(3a+b)-6a=

2. wyznacz x ze wzoru
a=bx+c
a=bx+c/d+e
1/a=1/b+1/x

3. oblicz wartosc funkcji dla danego argumentu
h(x)=x-1/x+2 dla x=3/7
g(x)=x+1/x-1 dla x=√3
f(x)=-x²+x³ dla x=-2⅔

Answer 1

(a-3b)²-2(a+b)(3a-b)-6b²=a²-6ab+9b²-2(3a²-ab+3ab-b²)-6b²=
=a²-6ab+9b²-6a²+2ab-6ab+2b²-6b²=-5a²-10ab+5b²
5(-a²-2ab+b²)

(a-b)²-(3a+2b)(3b-2a)=a²-2ab+b²-9ab+6a²-6b²+4ab=
=7a²-7ab-5b²

(a-4b)²-(3a+b)(b-2a)=a²-8ab+16b²-3ab+6a²-b²+2ab=
=7a²-9ab+15b²

(2a+b)²-2(a-b)(3a+b)-6a=4a²+4ab+b²-2(3a²+ab-3ab-b²)-6a=
=4a²+4ab+b²-6a²-2ab+6ab+2b²-6a=-2a²+8ab+3b²-6a

Answer 2

Zad 1
a) (a-3b)²-2(a+b)(3a-b)-6b²=a²-9b²-2(3a²-ab+3ab-b²)-6b²=a²-9b²-6a²-2ab+6ab-2b²-6b²=-5a²-17b²+4ab
b)(a-b)²-(3a+2b)(3b-2a)=a²-2ab+b²-9ab-6a²+6b²-4ab=-5a²+7b²-15ab
c)(a-4b)²-(3a+b)(b-2a)=a²-8ab+16b²-3ab-6a²+b²-2ab=-5a²+17b²-10ab
d)(2a+b)²-2(a-b)(3a+b)-6a=4a²+4ab+b²-3a²+ab-3ab-b²=a²+2ab
Zad.2
a)a=bx+c /-c
a-c=bx /:b
a-c/b=x
b)a=bx+c/d+e /-e
a-e=bx+c/d /-d/c
a-e-d/c=bx /:b
(a-e-d/c)/b=x
c)1/a=1/b+1/x /*x/1
1/a*x=1/b /*a/1
x=1/b*a
x=a/b