Sprowadź do najprostszej postaci i oblicz wartości liczbowe wyrażeń:

a) (3x - 1)² - 9x - (3x - 1)(3x+1)
dla x= -⅕
b) (x - 2y)(x + 2y) + (x + y)² - (x - y)² - 4y(x - y)
dla x= -5, y= ½
c) (2x + y)² - (x + 3)(x - 3) - (y² - 9)
dla x= -2, y= ½
d) -2a² - 16(a/2 - 1) + 3(a + 3)² - 27
dla a= -5
e) (2x - 3y)² - (3x + y)(3x - y) + (x - 2y)² - (8x - 7y) • (-2y)
dla x= 1, y= 100
f) 2(2a -3b)² - 3(a - 2b) • (a + 2b) + 12ab
dla a= 3√6, b = -√2

2

Odpowiedzi

Najlepsza Odpowiedź!
2009-12-04T16:38:28+01:00
A) (3x - 1)² - 9x - (3x - 1)(3x+1)=
=9x²-6x+1-9x-9x²+1=
=-15x+2
dla x=-1/5
-15(-1/5)+2=5
b)(x - 2y)(x + 2y) + (x + y)² - (x - y)² - 4y(x - y)= =x²-4y²+x²+2xy+y²-(x²-2xy+y²)-4xy+4y²=
= x²-4y²+x²+2xy+y²-x²+2xy-y²-4xy+4y²=
=x²
(-5)²=25
c) (2x + y)² - (x + 3)(x - 3) - (y² - 9)=
=4x²+4xy+y²-x²+9-y²+9=
= 3x²+4xy+18
12-4+18=26
d) -2a² - 16(a/2 - 1) + 3(a + 3)² - 27=
= -2a²-8a+16+3a²+18a+27-27=
= a²+10a+16
25-50+16=-25+16=-9
e) (2x - 3y)² - (3x + y)(3x - y) + (x - 2y)² - (8x - 7y) • (-2y)= =4x²-12xy+9y²-9x²+y²+x²-4xy+4y²+16xy-14y²=
=-5x²
-5(1)²=-5
f) 2(2a -3b)² - 3(a - 2b) • (a + 2b) + 12ab= =8a²-24ab+18b²-3a²+12b²+12ab=
=5a²+30b²-12ab
dla a= 3√6, b = -√2
270+60-12(3√6*(-√2))=330+36√12
1 5 1
2009-12-04T22:38:05+01:00
A.(3x-1)²-9x-(3x-1)(3x+1)=9x²-6x+1-9x-9x²+1= -15x+2
-15(-1/5)+2=5
b.(x-2y)(x+2y)+(x+y)²-(x-y)²-4y(x-y)= x²-4y²+x²+2xy+y²-(x²-2xy+y²)-4xy+4y² = x²-4y²+x²+2xy+y²-x²+2xy-y²-4xy+4y²
(-5)²=25
c.(2x+y)²-(x+3)(x-3)-(y²-9)= 4x²+4xy+y²-x²+9-y²+9 = 3x²+4xy+18
12-4+18=26
d.-2a²-16(a/2-1)+3(a+3)²-27 = -2a²-8a+16+3a²+18a+27-27 = a²+10a+16
25-50+16=-25+16=-9
e.(2x-3y)²-(3x+y)(3x-y)+(x-2y)²-(8x-7y)(-2y) = 4x²-12xy+9y²-9x²+y²+x²-4xy+4y²+16xy-14y² = -5x²
-5(1)²=-5
f. 2(2a -3b)²-3(a-2b)(a+2b)+12ab = 8a²-24ab+18b²-3a²+12b²+12ab = 5a²+30b²-12ab
a= 3√6 b = -√2
270+60-12(3√6*(-√2))=330+36√12