cho da thuc A=(x+2)(x+4)(x+6)(x+8).
a/ Tim GTNN cua A
b/CM A+16 la so chinh phuong voi moi x thuoc Z
c/Tim du khi chia A cho x^2+10x+5
d/tim x de A=105
cho da thuc A=(x+2)(x+4)(x+6)(x+8). a/ Tim GTNN cua A b/CM A+16 la so chinh phuong voi moi x thuoc Z c/Tim du khi chia A cho x^2+10x+5 d/tim x de A=10
By aikhanh
Đáp án:
Giải thích các bước giải:
\[\begin{array}{l}
A = (x + 2)(x + 4)(x + 6)(x + 8) = \left[ {\left( {x + 2} \right)\left( {x + 8} \right)} \right]\left[ {\left( {x + 4} \right)\left( {x + 6} \right)} \right] = \left( {{x^2} + 10x + 16} \right)\left( {{x^2} + 10x + 24} \right) = \left( {{x^2} + 10x + 20 – 4} \right)\left( {{x^2} + 10x + 20 + 4} \right) = {\left( {{x^2} + 10x + 20} \right)^2} – 16\\
a)Ta\_co:{\left( {{x^2} + 10x + 20} \right)^2} \ge 0 = > A \ge – 16 = {A_{\min }} = – 16 \Leftrightarrow {x^2} + 10x + 20 = 0 \Leftrightarrow x = – 5 \pm \sqrt 5 \\
b)A + 16 = {\left( {{x^2} + 10x + 20} \right)^2} = > A + 16\_la\_so\_chinh\_phuong\_voi\_moi\_x \in Z\\
c)A = {x^4} + 20{x^3} + 140{x^2} + 400x + 384 = ({x^2} + 10x + 5).({x^2} + 10x + 35) + 100x + 209\\
= > so\_du:100x + 209\\
d)A = 105 = > {\left( {{x^2} + 10x + 20} \right)^2} – 16 = 105\\
\Leftrightarrow {({x^2} + 10x + 20)^2} = 121\\
\Rightarrow \left[ \begin{array}{l}
{x^2} + 10x + 20 = 11\\
{x^2} + 10x + 20 = – 11
\end{array} \right. = > \left[ \begin{array}{l}
x = – 1\\
x = – 9
\end{array} \right.
\end{array}\]