B=121-[2^4-(4^2+889)
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\(B=121-\left[2^4-\left(4^2+889\right)\right]\)
\(\Rightarrow B=121-2^4+\left(4^2+889\right)\)
\(\Rightarrow B=121-2^4+4^2+889\)
\(\Rightarrow B=121-16+16+889\)
\(\Rightarrow B=121+889\)
\(\Rightarrow B=1010\)
a, 25*5*13*4=6500
87*125*8*4=348000
b,50*76*2=7600
19*4*25*8=15200
c,303*20*6*5=181800
4*889*25=88900
889 x 2 = 1778
5689 x 4 = 22756
2873 x 8 = 22984
4638 x 7 = 32466
\(\frac{\frac{2}{7}+\frac{2}{9}-\frac{2}{121}}{\frac{4}{7}+\frac{4}{9}-\frac{4}{121}}=\frac{2.\hept{ }\frac{1}{7}+\frac{1}{9}-\frac{1}{121}}{4.\hept{ }\frac{1}{7}+\frac{1}{9}-\frac{1}{121}}=\frac{2}{4}=\frac{1}{2}\)
bạn nhớ thay ngoặc nhọn thành ngoặc tròn nhé và nhớ đóng mở ngoặc
a) \(\Rightarrow\left(\dfrac{1}{2}x-\dfrac{1}{3}\right)^2=\dfrac{4}{25}\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{1}{2}x-\dfrac{1}{3}=\dfrac{2}{5}\\\dfrac{1}{2}x-\dfrac{1}{3}=-\dfrac{2}{5}\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{22}{15}\\x=-\dfrac{2}{15}\end{matrix}\right.\)
b) \(\Rightarrow\left(1-\dfrac{1}{4}x\right)^2=\dfrac{121}{49}\)
\(\Rightarrow\left[{}\begin{matrix}1-\dfrac{1}{4}x=\dfrac{11}{7}\\1-\dfrac{1}{4}x=-\dfrac{11}{7}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{16}{7}\\x=\dfrac{72}{7}\end{matrix}\right.\)
\(B=1+2+4+5+7+8+10+...+119+121+122\)
Ta có :
\(A=1+2+3+...+121+122\)
\(A=\left[\left(122-1\right):1+1\right]\left(1+122\right):2\)
\(A=122.\left(123\right):2=7503\)
Ta lại có :
\(C=3+6+9+...+120\)
\(C=\left[\left(120-3\right):3+1\right]\left(3+120\right):2\)
\(C=40.123:2=2460\)
Ta thấy : \(B=A-C\)
\(B=7503-2460=5043\)
Tổng quát:
\(\dfrac{1}{\left(n+1\right)\sqrt{n}+n\sqrt{n+1}}\)\(=\dfrac{1}{\sqrt{n\left(n+1\right)}\left(\sqrt{n+1}+\sqrt{n}\right)}\)
\(=\dfrac{\sqrt{n+1}-\sqrt{n}}{\sqrt{n\left(n+1\right)}}\)\(=\dfrac{1}{\sqrt{n}}-\dfrac{1}{\sqrt{n+1}}\)
\(\Rightarrow S=\dfrac{10}{11}\)
Ta có công thức tổng quát như sau:
\(\dfrac{1}{\left(n+1\right)\sqrt{n}+n\sqrt{n+1}}\)
\(=\dfrac{\left(n+1\right)\sqrt{n}-n\sqrt{n+1}}{\left[\left(n+1\right)\sqrt{n}+n\sqrt{n+1}\right]\left[\left(n+1\right)\sqrt{n}-n\sqrt{n+1}\right]}\)
\(=\dfrac{\left(n+1\right)\sqrt{n}-n\sqrt{n+1}}{n\left(n+1\right)^2-n^2\left(n+1\right)}\)
\(=\dfrac{\sqrt{n}}{n}-\dfrac{\sqrt{n+1}}{n+1}\)
\(=\dfrac{1}{\sqrt{n}}+\dfrac{1}{\sqrt{n+1}}\)
Áp dụng vào tổng S ta có:
\(S=\dfrac{1}{2\sqrt{1}+1\sqrt{2}}+\dfrac{1}{3\sqrt{2}+2\sqrt{3}}+...+\dfrac{1}{121\sqrt{120}+120\sqrt{121}}\)
\(S=\dfrac{1}{\sqrt{1}}-\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{2}}-\dfrac{1}{\sqrt{3}}+...+\dfrac{1}{\sqrt{120}}+\dfrac{1}{\sqrt{121}}\)
\(S=1-\dfrac{1}{\sqrt{121}}=1-\dfrac{1}{11}=\dfrac{10}{11}\)
B= 121-[16-(16+889)]
B= 121-[16-905]
B= 121+889
B= 1010
Giải:
\(B=121-\left[2^4-\left(4^2+889\right)\right]\)
\(\Leftrightarrow B=121-\left[16-\left(16+889\right)\right]\)
\(\Leftrightarrow B=121-16+16+889\)
\(\Leftrightarrow B=121+889\)
\(\Leftrightarrow B=1010\)