rút gọn biểu thức
M= {[2/7+2/5+2/17-2/239_3/7+3/5+3/17-3/239}:{7/12+5/6-1_5-3/4+1/3}]
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rút gọn
rút gọn biểu thức M = [ {2/7 + 2/5 + 2/17 - 2/239 _ 3/7 + 3/5 + 3/17 - 3/239 } : { 7/12 + 5/6 - 1 _ 5 - 3/4 + 1/3} ] . 27/11
chú thích :
/ : là gạch p/s nha
còn dấu _ : là tất cả trên
thu gọn các biểu thức sau
a)C=3^14+3^15+3^16+3^17+...+3^n
b)D=3^11+3^14+3^17+3^20+...+3^2021
c) E= -5^2-5^4-5^6-5^8-...-5^1000
d)F=-5^21-5^23-5^25-5^27-...-5^2019
e)M=7^2-7^4+7^6-7^8+...-7^1000
d)N=-12+11^2+11^3-11^4-11^5+...+11^498+11^499
b: \(27D=3^{14}+3^{17}+...+3^{2024}\)
\(\Leftrightarrow26D=3^{2024}-3^{11}\)
hay \(D=\dfrac{3^{2024}-3^{11}}{26}\)
c: \(25E=-5^4-5^6-...-5^{1002}\)
\(\Leftrightarrow24E=-5^{1002}+5^2\)
hay \(E=\dfrac{-5^{1002}+5^2}{24}\)
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B 5. Rút gọn các biểu thức sau:
a)\(\sqrt{7+4\sqrt{3}}\) b)\(\sqrt{9-4\sqrt{5}}\)
c)\(\sqrt{14+6\sqrt{5}}\) d)\(\sqrt{17-12\sqrt{2}}\)
a.\(\sqrt{7+4\sqrt{3}}=\sqrt{\left(\sqrt{3}+2\right)^2}=\left|\sqrt{3}+2\right|=\sqrt{3}+2\)
b.\(\sqrt{9-4\sqrt{5}}=\sqrt{\left(\sqrt{5}-2\right)^2}=\left|\sqrt{5}-2\right|=\sqrt{5}-2\)
c.\(\sqrt{14+6\sqrt{5}}=\sqrt{\left(\sqrt{5}+3\right)^2}=\left|\sqrt{5}+3\right|=\sqrt{5}+3\)
d.\(\sqrt{17-12\sqrt{2}}=\sqrt{\left(2\sqrt{2}-3\right)^2}=\left|2\sqrt{2}-3\right|=3-2\sqrt{2}\)
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Rút gọn biểu thức:
A = 2/7 + 2/5 + 2/17 - 2/293
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3/7 + 3/5 + 3/17 + 3/293
\(A=\frac{\frac{2}{7}+\frac{2}{5}+\frac{2}{17}-\frac{2}{293}}{\frac{3}{7}+\frac{3}{5}+\frac{3}{17}-\frac{3}{293}}\)
\(A=\frac{2.\left(\frac{1}{7}+\frac{1}{5}+\frac{1}{17}-\frac{1}{293}\right)}{3.\left(\frac{1}{7}+\frac{1}{5}+\frac{1}{17}-\frac{1}{293}\right)}\)
\(A=\frac{2}{3}\)
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Tính giá trị biểu thức: a) A= |-101|+|21|+|-99|-|25|. b) B= ||17-42|-64|. c) C= |2^7-7^2|+|3^3-3^4|+|10^3-3^5|. d) D= |1/3 - 2/3| + |5/6 + -7/12|
a; A = |-101| + |21| + |-99| - |25|
A = 101 + 21 + 99 - 25
A = (101 + 99) - (25 - 21)
A = 200 - 4
A = 196
b; B = ||17 - 42| - 64|
B = ||-25| - 64|
B = |25 - 64|
B = |-39|
B = 39
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c, C = |27 - 72| + |33 - 34| + |103 - 35|
C = |128 - 49| + |27 - 81| + |1000 - 243|
C = |79| + |-54| + | 757|
C = 79 + 54 + 757
C = 133 + 757
C = 890
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d; D = |\(\dfrac{1}{3}\) - \(\dfrac{2}{3}\)| + |\(\dfrac{5}{6}\) + (-\(\dfrac{7}{12}\))|
D = |-\(\dfrac{1}{3}\)| + |\(\dfrac{1}{4}\)|
D = \(\dfrac{1}{3}\) + \(\dfrac{1}{4}\)
D = \(\dfrac{7}{12}\)
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Rút gọn biểu thức sau:
A = \(\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
B = \(\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)
C = \(\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}\)
D = \(\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)
E = \(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
\(A=\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
\(=\sqrt{\left(2+\sqrt{3}\right)^2}-\sqrt{\left(2-\sqrt{3}\right)^2}\)
\(=|2+\sqrt{3}|-|2-\sqrt{3}|\)
\(=2+\sqrt{3}-2+\sqrt{3}\)
\(=2\sqrt{3}\)
\(B=\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)
\(=\sqrt{\left(3+\sqrt{2}\right)^2}-\sqrt{\left(3-\sqrt{2}\right)^2}\)
\(=|3+\sqrt{2}|-|3-\sqrt{2}|\)
\(=3+\sqrt{2}-3+\sqrt{2}\)
\(=2\sqrt{2}\)
\(C=\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}\)
\(=\sqrt{\left(3+2\sqrt{2}\right)^2}+\sqrt{\left(3-2\sqrt{2}\right)^2}\)
\(=|3+2\sqrt{2}|+|3-2\sqrt{2}|\)
\(=3+2\sqrt{2}+3-2\sqrt{2}\)
\(=6\)
\(D=\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)
\(=\sqrt{\left(2+\sqrt{5}\right)^2}-\sqrt{\left(2-\sqrt{5}\right)^2}\)
\(=|2+\sqrt{5}|-|2-\sqrt{5}|\)
\(=2+\sqrt{5}-\sqrt{5}+2\)
\(=4\)
\(E=\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
\(=\sqrt{\left(1+\sqrt{5}\right)^2}-\sqrt{\left(1-\sqrt{5}\right)^2}\)
\(=|1+\sqrt{5}|-|1-\sqrt{5}|\)
\(=1+\sqrt{5}-\sqrt{5}+1\)
\(=2\)
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\(A=\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
\(A=\sqrt{3}+2+2-\sqrt{3}\)
A = 2 + 2
A = 4
\(B=\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)
\(B=\sqrt{2}+3+3-\sqrt{2}\)
B = 3 + 3
B = 6
\(C=\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}\)
\(C=3+2\sqrt{2}+3-2\sqrt{2}\)
C = 3 + 3
C = 6
\(D=\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)
\(D=\sqrt{5}+2-\sqrt{5}+2\)
D = 2 + 2
D = 4
\(E=\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
\(E=\sqrt{5}+1-\sqrt{5}+1\)
E = 1 + 1
E = 2
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a) 5/7 + 4/3 + 2/7 + 5/3
b) 17/12 + 29/7 - 8/7 + 7/12
c) 2/5 + 6/9 + 7/4 + 3/5 + 1/3 + 1/4
d) 17/51 + 13/17 + 29/11 + 50/75 + 4/17 + 4/11
a: =(5/7+2/7)+(4/3+5/3)=3+1=4
b: =(17/12+7/12)+(29/7-8/7)
=2+3=5
c: =(2/5+3/5)+(6/9+1/3)+(7/4+1/4)
=1+2+1
=4
d: =(1/3+2/3)+(13/17+4/17)+(29/11+4/11)
=1+1+3=5
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Rút gọn:
1
1
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2
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1
2
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3
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1
3
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4
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1
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5
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1
5...
Đọc tiếp
Rút gọn: 1 1 - 2 - 1 2 - 3 + 1 3 - 4 - 1 4 - 5 + 1 5 - 6 - 1 6 - 7 + 1 7 - 8 - 1 8 - 9
Tính:
a) -5/7(14/5 - 7/10) : |-2/3| - 3/4(8/9 + 16/3) + 10/3(1/3 + 1/5)
b) 17/-26(1/6 - 5/3) : 17/13 - 20/3(2/5 - 1/4) + 2/3(6/5 - 9/2)
c) -8/9(9/8 - 3/2) + 5/4 : (5/2 - 15/4) - 3/4(10/9 - 8/3) : (-1/3)
d) 21/10 : (12/5 - 9/10) . (-4/7) - 3/2(1/6 - 7/12) + 1/5(3/2 - 1/4)
a) Ta có: \(\dfrac{-5}{7}\left(\dfrac{14}{5}-\dfrac{7}{10}\right):\left|-\dfrac{2}{3}\right|-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)+\dfrac{10}{3}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)
\(=\dfrac{-5}{7}\cdot\dfrac{3}{2}\cdot\dfrac{21}{10}-\dfrac{3}{4}\cdot\dfrac{56}{3}+\dfrac{10}{3}\cdot\dfrac{8}{15}\)
\(=\dfrac{-9}{4}-14+\dfrac{16}{9}\)
\(=\dfrac{-1621}{126}\)
b) Ta có: \(\dfrac{17}{-26}\cdot\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)
\(=\dfrac{-17}{26}\cdot\dfrac{13}{17}\cdot\dfrac{-3}{2}-\dfrac{20}{3}\cdot\dfrac{3}{20}+\dfrac{2}{3}\cdot\dfrac{-33}{10}\)
\(=\dfrac{3}{4}-1-\dfrac{11}{5}\)
\(=-\dfrac{49}{20}\)
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