Sprowadź wyrażenia do najprostszej postaci i oblicz ich wartość dla podanych obok wartości zmiennych :
a) 2(x - 3y)² - 3(x - 2y)(x + 2y_ + 12xy ; x= 3 , y= -1
b) 2(5x² + 4) + (2x - 3)(2x + 3) - 2 (3x-1)² + 3(1-2x)² ; x= -½

Sprowadź wyrażenia do najprostszej postaci :
a) 2(3x + √2)(3x - √2) + (√2x + √8)²
b) 2(3x - 5)² - (x + 3)³ + 3(x+1)(x² - x + 1)

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Odpowiedzi

2009-12-03T19:23:53+01:00
A) 2(x - 3y)² - 3(x - 2y)(x + 2y_ + 12xy ; x= 3 , y= -1
= 2(x² - 3xy + 9y²) -3(x² -4y²) +12xy =
= 2x² -6xy + 18y² -3x² +12y² +12xy =
= - x²+6xy + 30 y²

dla x =3 i y = -1
= - (3²) + 6*3*(-1) + 30*(-1)² =
= -9 - 18 -30 =
= - 57


b) 2(5x² + 4) + (2x - 3)(2x + 3) - 2 (3x-1)² + 3(1-2x)² ; x= -½
= 10x² +8 + 4x² - 9 -2(9x² - 6x +1) + 3( 1 - 4x +4x²)=
= 14x² -1 -18x² + 12x -2 + 3 -12x +12x²=
= 8x²

dla x = -½

= 8* (-½)² = 8*¼ = 2


a) 2(3x + √2)(3x - √2) + (√2x + √8)²
= 2(9x²-2) + ( 2x² +2*√2*√8 + 8) =
= 18x² - 4 +2x² + 2*√16 +8 =
= 18x² + 4 +2x² + 2*4 =
= 20x² +12

b) 2(3x - 5)² - (x + 3)³ + 3(x+1)(x² - x + 1) =
= 2( 9x² - 30x + 25) - ( x² +6x +9) + 3(x³ - x² +x +x² - x +1 )=
= 18x² -60x +5 - x² -6x -9 + 3(x³ +1) =
= 17x² -66x - 4 +3x³ +3 =
= 3x³ + 17x² -66x -1

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2009-12-03T19:29:14+01:00
A)(2x-6y)²-3x-6y+x²+2xy+12x²y= 4x-36y-3x-6y+x²+2xy+12x²y = x-42y+x²+2xy+12x²y = 3+42+9-12-108 = 42-108= -66

b)10x²+8+2x-3+4x²+6x-6x-(6x+2)²+(3-6x)² = 10x²+8+2x-3+4x²+36x+4+9+36x=14x² +74x + 25 = -7² + 37 +25 = -49 +37 +25 = 13

Tylko tyle byłam w stanie ;)
1 1 1
2009-12-03T19:53:21+01:00
A) 2(x - 3y)² - 3(x - 2y)(x + 2y_ + 12xy) ; x= 3 , y= -1
2(x²-2*x*(-3y)+(3y)²)-3(x²+2xy+12x²y-2xy-4y²-24xy²)
2(x²-6xy+9y²)-3x²-6xy-36x²y+6xy+12y²+72xy²
2x²-12xy+18y²-3x²-6xy-36x²y+6xy+12y²+72xy²
-x²+30y²-12xy-36x²y+72xy²
(-3)²+30*(-1)²-12*3*(-1)-36*3²*(-1)+72*3*(-1)²
9+30+36+324+216=615

b) 2(5x² + 4) + (2x - 3)(2x + 3) - 2 (3x-1)² + 3(1-2x)² ; x= -½
10x²+8+4x²-9-2(3x²-2*3x*(-1)+(-1)²)+3(1²-2*1*(-2x)+(-2x)²=
10x²+8+4x²-9-2(6x²+6x+1)+3(1+4x+4x²)=
10x²+8+4x²-9-12x²-12x-2+3+12x+12x²=
14x²=14*(-1/2)=14*1/4=3,5

a) 2(3x + √2)(3x - √2) + (√2x + √8)²=
2(9x²-20)+(√2x²)+2*√2x*8+(√8)²=
18x²-40+2x²+16*√2x+8=
20x²+16√2x-32

b) 2(3x - 5)² - (x + 3)³ + 3(x+1)(x² - x + 1)=
2(9x²-30x+25)-x³+3*x²*3+3*x*3²+3³+3(x³-x²+x+x²-x+1)=
18x²-60x+50-x³+9x²+27x+27+3(x³+1)=
18x²-60x+50-x³+9x²+27x+27+3x³+3=
2x³+27x²-33x+80




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