Đáp án:
1/ a/ $\text{$x=0$ hoặc $x=1$}$
b/ $x=2$
c/ $\text{$x=2$ hoặc $x=3$ hoặc $x=4$}$
2/ $A=\dfrac{3^{2021}-3}{2}$
3/ $a=39$
4/ $x=7$
Giải thích các bước giải:
1/ a/ $x^{11}=x$
$⇒ x^{11}-x=0$
$⇒ x(x^{10}-1)=0$
$⇒ \left[ \begin{array}{l}x=0\\x^{10}=1\end{array} \right.$
$⇒ \left[ \begin{array}{l}x=0\\x=1\end{array} \right.$
b/ $(2x+1)^3=125$
$⇒ 2x+1=5$
$⇒ 2x=4$
$⇒ x=2$
c/ $(x-3)^8=(x-3)^6$
$⇒ (x-3)^8-(x-3)^6=0$
$⇒ (x-3)^6.[(x-3)^2-1]=0$
$⇒ (x-3)^6.(x^2-6x+8)=0$
$⇒ (x-3)^6.(x^2-2x-4x+8)=0$
$⇒ (x-3)^6.(x-2)(x-4)=0$
$⇒ \left[ \begin{array}{l}x=3\\x=2\\x=4\end{array} \right.$
2/ $A=3+3^2+3^3+.....+3^{2020}$
$⇒ 3A=3^2+3^3+3^4+.....+3^{2021}$
$⇒ 3A-A=(3^2+3^3+3^4+.....+3^{2021})-(3+3^2+3^3+.....+3^{2020})$
$⇒ 2A=3^{2021}-3$
$⇒ A=\dfrac{3^{2021}-3}{2}$
3/ $2a+3=3^4$
$⇒ 2a=81-3$
$⇒ 2a=78$
$⇒ a=39$
4/ $(x+1)+(x+2)+(x+3)+.....+(x+100)=5750$
$⇒ 100x+(1+2+3+....+100)=5750$
$⇒ 100x+(100+1).50=5750$
$⇒ 100x=5750-5050$
$⇒ 100x=700$
$⇒ x=7$
Chúc bạn học tốt !!!
