Zastosuj wzór skróconego mnożenia do rozwiązywania równań. a)b) c) d) e)f) g)h).... Question from @Olamoskwa15

December 2018 1 17 Report

Zastosuj wzór skróconego mnożenia do rozwiązywania równań.

a) $(x+3)^{2} - (4-x)(4+x)=2( x-1)^{2} +1$
b) $12-2( x-1)^{2} =4(x-2)-(x-3)(2x-5)$
c) $5( x-1)^{2} -2( x+3)^{2} =3( x+2)^{2} -7(6x-1)$
d) $(3x-1)^{2} -5( 2x+1)^{2} +(6x-3)(2x+1)=(x-1)$
e) $(x+5)(x-5)-(x-3)(x+4)=x+1$
f) $(2-x)(2+x)+ (x+3)^{2} =x-7$
g) $( x+3)^{2} -(x+3)(x-3)=5$
h) $(x+3)^{2} -(4-x)(4+x)=2( x-1)^{2} +1$

krysta $a)\\\\ (x+3)^{2} - (4-x)(4+x)=2( x-1)^{2} +1\\\\x^2+6x+9 -(16-x^2) =0\\\\x^2+6x+9 - 16+x^2 =0\\\\ 6x=6\ \ /:6 \\ \\x=1$

$b) \\\\12-2( x-1)^{2} =4(x-2)-(x-3)(2x-5) \\\\ 12-2( x^2-2x+1) =4 x-8-(2x^2-5x-6x+15)\\\\ 12-2 x^2+4x- 2 =4 x-8- 2x^2+11x- 15 \\\\ -2 x^2+4x- 4 x + 2x^2-11x =-8- 15-12+2 \\\\ -11x =-33 \ \ /:(-11)\\\\x=3$

$c)\\\\ 5( x-1)^{2} -2( x+3)^{2} =3( x+2)^{2} -7(6x-1)\\\\ 5( x^2-2x+1) -2( x^2+6x+9 ) =3( x^2+4x+4 ) -42x+7\\\\ 5 x^2-10x+5 -2 x^2-12x-18 =3 x^2+12x+12 -42x+7\\\\ 5 x^2-10x -2 x^2-12x - 3 x^2-12x+42x= 12 +7-5 +18\\\\ 8x= 32\ \ / : 8\\\\x=4$

$d)\\\\ (3x-1)^2 -5( 2x+1)^2 +(6x-3)(2x+1)=(x-1)(x+1) \\\\9x^2-6x+1 -5( 4x^2+4x+1) +(12x^2+6x-6x-3) =x^2-1 \\\\9x^2-6x+1 -20x^2-20x-5 + 12x^2+6x-6x-3 =x^2-1 \\\\9x^2-6x -20x^2-20x + 12x^2+6x-6x-x^2=-1-1+5+3\\\\ -26x =6 \ \ /:(-26)\\\\x=-\frac{6}{26}\\\\x=-\frac{3}{13}$

$e)\\\\(x+5)(x-5)-(x-3)(x+4)=x+1\\\\ x^2-25-(x^2+4x-3x-12 ) =x+1 \\\\x^2-25- x^2-4x+3x+12 =x+1 \\\\ - x-x = 1+25-12\\\\-2x=14 \ \ / :(2)\\\\x=-7$

$f)\\\\ (2-x)(2+x)+ (x+3)^{2} =x-7\\ 4-x^2 + x^2+6x+9 =x-7\\ \\ 6x-x = -7-4-9\\\\5x=-20 \ \ / :5 \\\\x=-4$

$g)\\\\( x+3)^{2} -(x+3)(x-3)=5 \\\\x^2+6x+9 -(x^2-9)=5 \\\\x^2+6x+9 - x^2+9 =5 \\ \\ 6x =5 -9-9\\\\6x=-13 \ \ /:6 \\\\x=-\frac{13}{6}$

$h)\\\\ (x+3)^{2} -(4-x)(4+x)=2( x-1)^{2} +1\\\\ x^2+6x+9 -(16-x^2) =2( x^2-2x+1 ) +1\\\\ x^2+6x+9 - 16+x^2 =2 x^2-4x+2 +1\\\\x^2+6x +x^2 -2 x^2+4x=2 +1-9 +16\\\\ 10x=10\ \ / :10\\\\x=1$

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