Question

Zad 1.) (2x-4y)(2x+4y)+(2x+4y)²+(2x-4y)²-(x-3)(x+7)=

dla x= -⅓
dlay= 3
-------------------------------------------------------
zad2). -(x-4)²=(3-x)(3+x) plus sprawdzenie

zad3.) (x+½)²-(x-1)(x+1)=16 plus sprawdzenie

Answer 1

Zad 1.) (2x-4y)(2x+4y)+(2x+4y)²+(2x-4y)²-(x-3)(x+7)=
stosuję wzory :
1) (a-b)(a+b) = a² -b²
2) (a +b)² = a² + 2ab + b²
3) (a -b)² = a² -2ab +b²

4x² - 16y² + 4x² + 16xy + 16y² + 4x² - 16xy + 16y² -(x²+4x -21)=
= 12x² +16y² -x² -4x +21 =
= 11x² + 16y² -4x +21

dla x= -⅓
dlay= 3

= 11*(-⅓)² + 16*3² -4*(-⅓) + 21=
= 11/9 + 144 + 4/3 +21=
= 11/9 +12/9 + 165 =
= 23/9+ 165=
= 2 i 5/9 + 165 =
= 167 i 5/9

zad2). -(x-4)²= (3-x)(3+x) plus sprawdzenie
-(x-4)²= (3-x)(3+x) /*(-1)
(x -4)² = x² -9
x² - 8x +16 = x² -9
x² - 8x +16 - x² + 9 =0
- 8x +25 = 0
- 8x = -25
x = 25/8
Spr.
L(25/8) = (25/8 -4)² = (3⅛ -4)² = (-⅞)² = 49/64
P(25/8) = ( 25/8-3)(25/8 +3)= ( 3⅛ - 3)( 3⅛ +3) = (⅛)(6⅛)=(⅛)(49/8)= 49/64
L(25/8) = P (25/8)


zad3.) (x+½)²-(x-1)(x+1)=16 plus sprawdzenie
x² + x +¼ -( x² -1) = 16
x² +x + ¼ - x² + 1 = 16
x = 16 -1¼
x = 14¾
x = 59/4
L(59/4) = (59/4 + ½)² - [ (59/4 )² -1] =
= (59/4 +2/4)² -[ 3481/16 - 16/16]=
= (61/4)² - [ 3465/16] = 3721/16 - 3465/16 = 256/16 = 16
P(59/4) = 16
L(59/4) = P(59/4)