Question

Rozwiąż nastepujące równania :

a) 1,2x²+(x+5)²-2(x+7)(x-7)=(x-6)²

b) (2x-3)²-(1-x)(1+x)+x=(3x-1)²+(1-2x)(2x+1)-9

c) (x-⅓)²-(x+2)(x-2)+ ⁸/₉ = (x+5)²- x²- ⅔x

odpowiedzi do zadań :
a) -4
b) 3
c) -2

Answer 1

A) 1+2x²+(x+5)²-2(x+7)(x-7)=(x-6)²
1+2x²+x²+2*5*x+25-2(x²-7²)=x²-2*x*6+6²
1+2x²+x²+10x-2x²+25+98=x²-12x+36
2x²+x²-2x²-x²+10x+12x+1+25+98-36=0
22x+88=0
22x=-88 /:22
x=-4
w zadaniu musi być 1+2x²....., a nie 1,2x²

b) (2x-3)²-(1-x)(1+x)+x=(3x-1)²+(1-2x)(2x+1)-9
4x²-2*2x*3+9-(1²-x²)+x=9x²-2*3x*1+1²+(1²-4x²)-9
4x²-12x+9-1+x²+x=9x²-6x+1+1-4x²-9
4x²+x²-9x²+4x²-12x+x+6x+9-1-1-1+9=0
-5x+15=0
-5x=-15 /:(-5)
x=3
c) (x-⅓)²-(x+2)(x-2)+ ⁸/₉ = (x+5)²- x²- ⅔x
x²-2*x*⅓+⅓²-(x²-2²)+8/9=x²+2*x*5+5²-x²-⅔x
x²-⅔x+1/9-x²+4+8/9=x²+10x+25-x²-⅔x
x²-x²-x²+x²-⅔x-10x+⅔x=25-1/9-4-8/9
-10x=20 /:(-10)
x=-2