GIÚP MÌNH VỚI
tính giá trị biểu thức
a) 1,6^2+4.0,8.3,4^2
b) 3^4.5^4 – (15^2 + 1) (15^2-1)
c) x^4 – 12x^3 + 12x^2 – 12x + 111 tại x=11
d) 5x(4x^2 – 2x +1) – 2x(10x^2 -5x -2)
e) 2004^2 – 16
g) 892^2 + 892 . 216 +108^2
GIÚP MÌNH VỚI tính giá trị biểu thức a) 1,6^2+4.0,8.3,4^2 b) 3^4.5^4 – (15^2 + 1) (15^2-1) c) x^4 – 12x^3 + 12x^2 – 12x + 111 tại x=11 d) 5x(4x^2 – 2x
By Maria
$a,$ $1,6^2 + 4.0,8.3,4^2$
$=$ $2,56 + 3,2.11,56$
$=$ $2,56 + 36,992$
$=$ $39,552$
$b,$ $3^4.5^4 – (15^2 + 1)(15^2 – 1)$
$=$ $81.625 – 15^4 + 1$
$=$ $50625 – 50625 + 1$
$=$ $1$
$c,$ $x^4 – 12x^3 + 12x^2 – 12x + 111$
$=$ $x^4 – 12x(x^2 – x + 1) + 111$
Thay $x$ $=$ $11$
$=$ $11^4 – 12.11.(11^2 – 11 + 1) + 111$
$=$ $14641 – 132.(120 – 10) + 111$
$=$ $14641 – 132.110 + 111$
$=$ $14641 – 14520 + 111$
$=$ $121 + 111$
$=$ $232$
$d,$ $5x(4x^2 – 2x + 1) – 2x(10x^2 – 5x – 2)$
$=$ $20x^3 – 10x^2 + 5x – 20x^3 + 10x^2 + 4x$
$=$ $9x$
$e,$ $2004^2 – 16$
$=$ $(2004 – 4)(2004 + 4)$
$=$ $2000.2008$
$=$ $4016000$
$g,$ $892^2 + 892.216 + 108^2$
$=$ $892^2 + 892.108.2 + 108^2$
$=$ $(892 + 108)^2$
$=$ $1000^2$
$=$ $1000000$
Học tốt nhé!
Giải thích các bước giải:
a, Sai đề
\(\begin{array}{l}
b,\\
{3^4}{.5^4} – \left( {{{15}^2} + 1} \right)\left( {{{15}^2} – 1} \right)\\
= {\left( {3.5} \right)^4} – \left[ {{{\left( {{{15}^2}} \right)}^2} – 1} \right]\\
= {15^4} – {15^4} + 1 = 1\\
c,\\
{x^4} – 12{x^3} + 12{x^2} – 12x + 111\\
= \left( {{x^4} – 11{x^3}} \right) – \left( {{x^3} – 11{x^2}} \right) + \left( {{x^2} – 11x} \right) – \left( {x – 11} \right) + 100\\
= \left( {x – 11} \right)\left( {{x^3} – {x^2} + x – x} \right) + 100\\
x = 11 \Rightarrow {x^4} – 12{x^3} + 12{x^2} – 12x + 111 = 100\\
d,\\
5x\left( {4{x^2} – 2x + 1} \right) – 2x\left( {10{x^2} – 5x – 2} \right)\\
= 20{x^3} – 10{x^2} + 5x – 20{x^3} + 10{x^2} + 4x = 9x\\
e,\\
{2004^2} – 16 = {2004^2} – {4^2} = \left( {2004 – 4} \right)\left( {2004 + 4} \right) = 2000.2008 = 4016000\\
g,\\
{892^2} + 892.216 + {108^2} = {892^2} + 2.108.892 + {108^2} = {\left( {892 + 108} \right)^2} = {1000^2} = 1000000
\end{array}\)