Đáp án:
$2.18)
a) x=1\\
b) x=\dfrac{7}{2}\\
c) x=\dfrac{2}{15}\\
d) x=\dfrac{-11}{25}\\
2.20
a) A=279\\
b) B=\dfrac{1025}{8}\\
c)
C=1105\\
d)
D=1\\
e) E=52258$
Giải thích các bước giải:
$2.18)
a) (x-1)^3+(2-x)(4+2x+x^2)+3x(x+2)=16\\
\Leftrightarrow x^3-3x^2+3x-1+2^3-x^3+3x^2+6x=16\\
\Leftrightarrow (x^3-x^3)+(-3x^2+3x^2)+(3x+6x)-1+8=16\\
\Leftrightarrow 9x=16-7=9\\
\Leftrightarrow x=1\\
b) (x+2)(x^2-2x+4)-x(x^2-2)=15\\
\Leftrightarrow x^3+2^3-x^3+2x=15\\
\Leftrightarrow (x^3-x^3)+8+2x=15\\
\Leftrightarrow 2x=15-8=7\\
\Leftrightarrow x=\dfrac{7}{2}\\
c) (x-3)^3-(x-3)(x^2+3x+9)+9(x+1)^2=15\\
\Leftrightarrow x^3-3.x^2.3+3.x.3^2-3^3-(x^3-3^3)+9(x^2+2x+1)=15\\
\Leftrightarrow x^3-9x^2+27x-27-x^3+27+9x^2+18x+9=15\\
\Leftrightarrow (x^3-x^3)+(-9x^2+9x^2)+(27x+18x)+(-27+27+9)=15\\
\Leftrightarrow 45x=15-9\\
\Leftrightarrow x=\dfrac{6}{45}=\dfrac{2}{15}\\
d) x(x-5)(x+5)-(x+2)(x^2-2x+4)=3\\
\Leftrightarrow x(x^2-25)-(x^3+2^3)=3\\
\Leftrightarrow x^3-25x-x^3-8=3\\
\Leftrightarrow -25x=3+8=11\\
\Leftrightarrow x=\dfrac{-11}{25}\\
2.20
a) A=(7-x)(x^2+7x+49)-(64-x^3)\\
=7^3-x^3-64+x^3\\
=279\\
b) B=64-(x-4)(x^2+4x+16)\\
=64-(x^3-4^3)\\
=64-x^3+64\\
=128-x^3\\
\Rightarrow B(\dfrac{-1}{2})=128-\left ( \dfrac{-1}{2} \right )^3=128+\dfrac{1}{8}=\dfrac{1025}{8}\\
c)
C=8a^3-27b^3\\
=(2a)^3-(3b)^3\\
=(2a-3b)\left [ (2a)^2+2a.3b+(3b)^2 \right ]\\
=(2a-3b).\left ( 4a^2+6ab+9b^2 \right )\\
=(2a-3b).\left ( 4a^2-12ab+9b^2+18ab \right )\\
=(2a-3b).\left [ (2a-3b)^2+18ab \right ]\\
\Rightarrow C=5.(5+18.12)=1105\\
d)
D=a^3+b^3+6a^2b^2(a+b)+3ab(a^2+b^2)\\
=(a+b)(a^2-ab+b^2)+6a^2b^2.1+3ab\left [ (a^2+b^2+2ab)-2ab \right ]\\
=1.(a^2-ab+b^2)+6a^2b^2+3ab\left [ (a+b)^2-2ab \right ]\\
=a^2-ab+b^2+6a^2b^2+3ab(1-2ab)\\
=a^2-ab+b^2+6a^2b^2+3ab-6a^2b^2\\
=a^2+(-ab+3ab)+b^2+\left (6a^2b^2-6a^2b^2 \right )\\
=a^2+2ab+b^2\\
=(a+b)^2\\
=1\\
e) E=(3x-1)(9x^2-3x+1)-(1-3x)(1+3x+9x^2)\\
=(3x-1)(9x^2-3x+1)+(3x-1)(1+3x+9x^2)\\ =(3x-1)(9x^2-3x+1+1+3x+9x^2)\\ =(3x-1)(18x^2+2)\\
\Rightarrow E(10)= (3.10-1).(18.10^2+2)=52258$
