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ta có : \(A=100^2+200^2+300^2+...+1000^2\)
\(A=\left(1.100\right)^2+\left(2.100\right)^2+\left(3.100\right)^2+...+\left(10.100\right)^2\)
\(A=100^2\left(1^2+2^2+3^3+...+10^2\right)\)
\(A=10000.385=3850000\)
vậy \(A=3850000\)
Ta có:A=1002+2002+3002+...+10002
=1002.12+1002.22+1002.32+...+1002.102
=1002(12+22+32+...102)
=10000.385
=3850000
=
A=1002.12+1002.22+1002.32+...+1002.102
=1002(12+22+32+...+102)=1002.385=3850000
ta có:A= 1002+2002+3002+...+10002
A=1002.(12+22+32+..102)
A=10000.385
A=3850000
\(A=100^2+200^2+300^2+...+1000^2\)
\(\Rightarrow A=100\left(1^2+2^2+3^2+...+10^2\right)\)
mà \(1^2+2^2+3^2+...+10^2=385\)
\(\Rightarrow A=100.385\)
\(\Rightarrow A=38500\)
Vậy .............
\(100^2+200^2+300^2+.....+1000^2\)
\(=\left(100\times1\right)^2+\left(100\times2\right)^2+.....+\left(100\times10\right)^2\)
\(=100^2\times1^2+100^2\times2^2+.....+100^2\times10^2\)
\(=100^2\left(1^2+2^2+3^2+.....+10^2\right)\)
\(=10000\times385\)
\(=3850000\)
Kaito Kid lm chưa chính xác lắm nhg dù sao chúc cả 2 bn học tốt.
A = 1002 + 2002 + 3002 + ... + 10002
= (1 . 100)2 + (2 . 100)2 + (3 . 100)2 + ... + (10 . 100)2
= 12 . 1002 + 22 . 1002 + 32 . 1002 + ... + 102 . 1002
= 10000(12 + 22 + 32 + ... 102)
Mà theo đề bài, 12 + 22 + 32 + ... 102 = 385 nên 10000(12 + 22 + 32 + ... 102) = 10000 . 385
= 3850000
a)Có: (x4)3=\(\dfrac{x^{15}}{x^5}\)
<=> x12=x10
<=> x12-x10=0
<=> x10(x2-1)=0
<=> \(\left[{}\begin{matrix}x^{10}=0\\x^2-1=0\end{matrix}\right.\)<=>\(\left[{}\begin{matrix}x=0\\x^2=1\end{matrix}\right.< =>\left[{}\begin{matrix}x=0\\x\in\left\{1;-1\right\}\end{matrix}\right.\)
Vậy x\(\in\left\{1;-1;0\right\}\)
b)Có 2x+2x+3=144
<=> 2x(1+23)=144
<=> 2x=16=24
=> x=4
c) Có \(1^2+2^2+3^2+...+10^2=385\)
<=> \(100^2\left(1^2+2^2+3^2+...+10^2\right)=385.100^2\)
<=> \(100^2.1^2+100^2.2^2+...+100^2.10^2=3850000\)
<=> \(100^2+200^2+...+1000^2=3850000\)
A=3,85.10^6
Ta có : 12 + 22 + 32 + ..... + 102 = 385
=> 1002(12 + 22 + 32 + ..... + 102) = 385
<=> 1002 + 2002 + 3002 + .... + 10002 = 385 . 1002
<=> 1002 + 2002 + 3002 + .... + 10002 = 3850000
\(\left(\frac{x-y}{\sqrt{x}-\sqrt{y}}-\frac{x\sqrt{x}-y\sqrt{y}}{x-y}\right)\) ):\(\left(\frac{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\right)\)
=\(\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}-\sqrt{y}}-\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)}{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}:\frac{x+\sqrt{xy}+y}{\sqrt{x}+\sqrt{y}}\)
=\(\left(\sqrt{x}+\sqrt{y}-\frac{x-\sqrt{xy}+y}{\sqrt{x}+\sqrt{y}}\right).\frac{\sqrt{x}+\sqrt{y}}{x+\sqrt{xy}+y}\)
=\(\frac{3\sqrt{xy}}{x+\sqrt{xy}+y}\)
Ta có:
\(100^2=1^2.100^2;200^2=2^2.100^2;.............;1000^2=10^2.100^2\)
\(\Rightarrow A=10000.\left(1^2+2^2+3^2+.....+10^2\right)\Rightarrow A=385.10000=3850000\)
A=1^2.100^2+2^2+100^2+3^2.100^2+...+10^2.100^2
A=(1^2+2^2+3^2+...10^2).100^2
A=385.10000=3850000