Đáp án:
\(\begin{array}{l}
c,\\
C = \dfrac{{999}}{{1000}}\\
d,\\
D = 17\\
e,\\
E = 999033
\end{array}\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
c,\\
C = {x^3} + 0,3{x^2} + 0,03x\\
= {x^3} + \dfrac{3}{{10}}{x^2} + \dfrac{3}{{100}}x\\
= \left( {{x^3} + 3.\dfrac{1}{{10}}{x^2} + 3.\dfrac{1}{{100}}x + \dfrac{1}{{1000}}} \right) - \dfrac{1}{{1000}}\\
= \left[ {{x^3} + 3.{x^2}.\dfrac{1}{{10}} + 3.x.{{\left( {\dfrac{1}{{10}}} \right)}^2} + {{\left( {\dfrac{1}{{10}}} \right)}^3}} \right] - \dfrac{1}{{1000}}\\
= {\left( {x + \dfrac{1}{{10}}} \right)^3} - \dfrac{1}{{1000}}\\
x = 0,9 \Rightarrow C = {\left( {0,9 + \dfrac{1}{{10}}} \right)^3} - \dfrac{1}{{1000}} = {1^3} - \dfrac{1}{{1000}} = \dfrac{{999}}{{1000}}\\
d,\\
{x^2} - x = 3 \Leftrightarrow {x^2} - x - 3 = 0\\
D = {x^4} - 2{x^3} + 3{x^2} - 2x + 2\\
= \left( {{x^4} - {x^3} - 3{x^2}} \right) + \left( { - {x^3} + {x^2} + 3x} \right) + \left( {5{x^2} - 5x - 15} \right) + 17\\
= {x^2}.\left( {{x^2} - x - 3} \right) - x.\left( {{x^2} - x - 3} \right) + 5.\left( {{x^2} - x - 3} \right) + 17\\
= \left( {{x^2} - x - 3} \right).\left( {{x^2} - x + 5} \right) + 17\\
= 0.\left( {{x^2} - x + 5} \right) + 17\\
= 17\\
e,\\
E = 27{x^3} + 27{x^2} + 10x - 999\\
= \left( {27{x^3} + 27{x^2} + 9x + 1} \right) + \left( {x - 1000} \right)\\
= \left( {27{x^3} + 3.9{x^2} + 3.3x + 1} \right) + \left( {x - 1000} \right)\\
= \left[ {{{\left( {3x} \right)}^3} + 3.{{\left( {3x} \right)}^2}.1 + 3.3x{{.1}^2} + {1^3}} \right] + \left( {x - 1000} \right)\\
= {\left( {3x + 1} \right)^3} + \left( {x - 1000} \right)\\
x = 33 \Rightarrow E = {\left( {3.33 + 1} \right)^3} + \left( {33 - 1000} \right)\\
= {100^3} + 33 - 1000\\
= 1000000 + 33 - 1000\\
= 1000033 - 1000\\
= 999033
\end{array}\)
