câu 1: thực hiền phép tính
A:=(2^2+4^2+6^2+...+70^2)-(1^2+3^2+5^2+...+69^2)
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VN
20 tháng 12 2022
a)
\(-12:\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2\)
\(=-12:\left(\dfrac{18}{24}-\dfrac{20}{24}\right)^2\)
\(=-12:\left(\dfrac{-1}{12}\right)^2\)
\(=-12:\dfrac{1}{144}\)
\(=-12\times\dfrac{144}{1}\)
\(=-1728\)
b)
\(\left(2^2:\dfrac{4}{3}-\dfrac{1}{2}\right)\times\dfrac{6}{5}-17\)
\(=\left(4\times\dfrac{3}{4}-\dfrac{1}{2}\right)\times\dfrac{6}{5}-17\)
\(=\left(3-\dfrac{1}{2}\right)\times\dfrac{6}{5}-17\)
\(=\dfrac{5}{2}\times\dfrac{6}{5}-17\)
\(=3-17\)
\(=-14\)
S
20 tháng 12 2022
a)\(=-12:\left(-\dfrac{1}{12}\right)^2\)
\(=-12:\dfrac{1}{144}\)\(=-12.144=-1728\)
b)\(=\left(8:\dfrac{4}{3}-\dfrac{1}{2}\right).\dfrac{6}{5}-17\)
\(=\left(6-\dfrac{1}{2}\right).\dfrac{6}{5}-17\)
\(=\dfrac{11}{2}.\dfrac{6}{5}-17=\dfrac{33}{5}-17=\dfrac{33}{5}-\dfrac{85}{5}=-\dfrac{2}{5}\)
16 tháng 8 2021
a: Ta có: \(3\sqrt{2}\cdot5\sqrt{6}\cdot4\sqrt{12}\)
\(=\sqrt{18\cdot25\cdot6\cdot16\cdot12}\)
\(=\sqrt{518400}\)
=720
b: Ta có: \(\left(\sqrt{7}-\sqrt{2}\right)^2+2\sqrt{14}\)
\(=9-2\sqrt{14}+2\sqrt{14}\)
=9
c: Ta có: \(\left(1+\sqrt{5}+\sqrt{6}\right)\left(1+\sqrt{5}-\sqrt{6}\right)\)
\(=6+2\sqrt{5}-6\)
\(=2\sqrt{5}\)
1 tháng 4 2022
Bài 2:
a: A=(12,87+14,13)+(-14,7-37,3)
=27-52=-25
b: B=-1/3+2/5-2/3-3/5+1/5
=-1
Y
8 tháng 7 2023
\(a,\dfrac{3}{5}-\dfrac{1}{2}\sqrt{1\dfrac{11}{25}}=\dfrac{3}{5}-\dfrac{1}{2}\sqrt{\dfrac{36}{25}}=\dfrac{3}{5}-\dfrac{1}{2}.\dfrac{\sqrt{6^2}}{\sqrt{5^2}}=\dfrac{3}{5}-\dfrac{1}{2}.\dfrac{6}{5}=\dfrac{3}{5}-\dfrac{6}{10}=\dfrac{3}{5}-\dfrac{3}{5}=0\)
\(b,\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)=5^2-\left(2\sqrt{6}\right)^2=25-2^2.\sqrt{6^2}=25-4.6=25-24=1\)
\(c,\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{4-2\sqrt{3}}\\ =\left|2-\sqrt{3}\right|+\sqrt{\sqrt{3^2}-2\sqrt{3}+1}\\ =2-\sqrt{3}+\sqrt{\left(\sqrt{3}-1\right)^2}\\ =2-\sqrt{3}+\left|\sqrt{3}-1\right|\\ =2-\sqrt{3}+\sqrt{3}-1\\ =1\)
\(d,\dfrac{\left(x\sqrt{y}+y\sqrt{x}\right)\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}}\left(dk:x,y>0\right)\\ =\dfrac{\left(\sqrt{x^2}.\sqrt{y}+\sqrt{y^2}.\sqrt{x}\right)\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}}\\ =\dfrac{\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}}\\ =\sqrt{x^2}-\sqrt{y^2}\\ =\left|x\right|-\left|y\right|\\ =x-y\)
25 tháng 6 2023
4:
a: =4/15-2,9+11/15=1-2,9=-1,9
b: \(=-36,75+3,7-63,25+6,3=10-100=-90\)
c: \(=6,5+3,5-\dfrac{10}{17}-\dfrac{7}{17}=10-1=9\)
d: \(=\dfrac{13}{25}\left(-39,1-60,9\right)=\dfrac{13}{25}\left(-100\right)=-52\)
e: =-5/12-7/12-3,7-6,3=-1-10=-11
f: =2,8(-6/13-7/13)-7,2=-2,8-7,2=-10
28 tháng 3 2021
\(a,\dfrac{2}{3}-\dfrac{5}{6}+\dfrac{3}{4}\)
\(=(\dfrac{2}{3}+\dfrac{3}{4})-\dfrac{5}{6}\)
\(=\dfrac{7}{12}\)
\(b,\dfrac{6}{7}.\dfrac{8}{13}+\dfrac{6}{13}.\dfrac{9}{7}-\dfrac{-4}{13}.\dfrac{6}{7}\)
\(=\dfrac{6}{7}.(\dfrac{8}{13}-\dfrac{4}{13})+(\dfrac{6}{13}.\dfrac{9}{7})\)
\(=(\dfrac{6}{7}.\dfrac{4}{13})+\dfrac{54}{91}\)
\(=\dfrac{24}{91}+\dfrac{54}{91}\)
\(=\dfrac{78}{91}=\dfrac{6}{7}\)
\(c,19.(-26)\)
\(=-494\)
TA
28 tháng 3 2021
a) `2/3 - 5/6 +3/4`
`=4/6-5/6+3/4`
`=-1/6+3/4`
`=-4/24+18/24`
`=14/24=7/12`
b) `6/7 .8/13 +6/13 .9/7 -4/13 .6/7`
`=6/7 .(8/13-4/13) + 6/13 .9/7`
`=6/7 . 4/13 + 6/13 . 9/7`
`= 6/13 .4/7 +6/13 .9/7`
`=6/13 . (4/7+9/7)`
`=6/13 . 13/7`
`=6/7`
c) `19.(-26)`
`=(1-20).(20+6)`
`=20+6-400-120`
`=-494`
24 tháng 8 2021
a)\(2\sqrt{\dfrac{16}{3}}-3\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
\(=2.\sqrt{\dfrac{4^2}{3}}-3.\sqrt{\dfrac{1}{3.3^2}}-6\sqrt{\dfrac{2^2}{3.5^2}}\)
\(=2.\dfrac{4}{\sqrt{3}}-3.\dfrac{1}{3\sqrt{3}}-6.\dfrac{2}{5\sqrt{3}}=\dfrac{8}{\sqrt{3}}-\dfrac{1}{\sqrt{3}}-\dfrac{12}{5\sqrt{3}}\)\(=\dfrac{23}{5\sqrt{3}}=\dfrac{23\sqrt{3}}{15}\)
b)\(\left(6\sqrt{\dfrac{8}{9}}-5\sqrt{\dfrac{32}{25}}+14\sqrt{\dfrac{18}{49}}\right).\sqrt{\dfrac{1}{2}}\)
\(=6\sqrt{\dfrac{8}{9}.\dfrac{1}{2}}-5\sqrt{\dfrac{32}{25}.\dfrac{1}{2}}+14\sqrt{\dfrac{18}{49}.\dfrac{1}{2}}\)
\(=6\sqrt{\dfrac{4}{9}}-5\sqrt{\dfrac{16}{25}}+14\sqrt{\dfrac{9}{49}}\)\(=6.\dfrac{2}{3}-5.\dfrac{4}{5}+14.\dfrac{3}{7}=6\)
c)\(\sqrt{\left(\sqrt{2}-2\right)^2}-\sqrt{6+4\sqrt{2}}=\left|\sqrt{2}-2\right|-\sqrt{4+2.2\sqrt{2}+2}=2-\sqrt{2}-\sqrt{\left(2+\sqrt{2}\right)^2}\)
\(=2-\sqrt{2}-\left(2+\sqrt{2}\right)=-2\sqrt{2}\)
Bài này hơi dài chờ mk giải nha
Đặt B = (2^2+4^2+6^2+...+70^2)
C = (1^2+3^2+5^2+...+69^2)
B = 2.2 + 4.4 + 6.6 + ... + 70 . 70
B = 2.(3-1) + 4.(5 - 1) + 6.(7-1) + ... + 70.(71 - 1)
B = 2 .3 - 2 + 4.5 - 4 + 6.7 - 6 + ... + 70 . 71 - 70
B = (2.3 + 4.5 + 6.7 + ... + 70.71) - (2 + 4 + 6 + ... + 70)
Đặt D = (2.3 + 4.5 + 6.7 + ... + 70.71)
E = (2 + 4 + 6 + ... + 70)
Ta có : D = 2.3 + 4.5 + 6.7 + ... + 70.71
3D = 2.3.3 + 4.5.3 + 6.7.3 + ... + 70.71.3
3D = 2.3.(4- 1) + 4.5.(6 - 3) + 6.7.(8 - 5) + ... + 70.71.(72 - 69)
3D = 2.3.4 - 2.3.1 + 4.5.6 - 4.5.3 + 6.7.8 - 6.7.5 + ... + 70.71.72 - 70.71.69
3D = (2.3.4 + 4.5.6 + ... + 70.71.72) - (2.3.1 + 4.5.3 + 6.7.5 + ... + 70.71.69 )
3D = 70.71.72
D = 70.71.72 : 3 = 119280
SSH của E là : (70 - 2) : 2 + 1 = 35 (SH)
Tổng E là : (2 + 70) . 35 : 2 = 1260
=> B = D - E = 119280 - 1260 = 118020
C = 1^2+3^2+5^2+...+69^2
C= 1.1 + 3.3 + 5.5 + ... + 69.69
C = 1.(2-1) + 3.(4 - 1) + ...+ 69.(70 - 1)
C = 1.2 - 1 + 3.4 - 3 + ... + 69 . 70 - 69
C = (1.2 + 3.4 + ... + 69.70) - (1 + 3 + ... + 69)
Đặt G = (1.2 + 3.4 + ... + 69.70)
H = (1 + 3 + ... + 69)
G = 1.2 + 3.4 + ... + 69.70
3G = 1.2.3 + 3.4.3 + ... + 69.70.3
3G = 1.2.3 + 3.4.(5-2) + ... + 69.70.(71 - 68)
3G = 1.2.3 + 3.4.5 - 3.4.2 + ... + 69.70.71 - 69.70.68
3G = (1.2.3 + 3.4.5 + ... + 69.70.71) - (3.4.2 + ... + 69.70.68)
3G = 69.70.71
=> G = 69.70.71 : 3 = 114310
SSH của H là : (69 - 1) : 2 + 1 = 35 (SH)