(3x -48) .6 =3^2 . 2^2 + 2^3 . 3^2 - 12
Làm giúp mk với !!=/
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a) \(\left(9^4.8+9^4.5\right):\left(9^2.\left(10-1\right)\right)\)
=\(9^4.13:9^3=13.9=117\)
b) 100-(75-25)=100-50=50
Đặt tổng trên = A
\(A=\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{98}+\frac{2}{192}\)
\(A.2=\frac{4}{3}+\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{98}\)
\(A.2-A=\left(\frac{4}{3}+\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{98}\right)-\left(\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{98}+\frac{2}{192}\right)\)
\(A=\frac{4}{3}-\frac{2}{192}\)
\(A=\frac{127}{96}\)
\(A=\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{98}+\frac{2}{192}\)
\(2A=\frac{4}{3}+\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{98}\)
\(2A-A=\frac{4}{3}-\frac{2}{192}\)
\(A=\frac{4}{3}-\frac{2}{192}=\frac{127}{96}\)
\(a,=\left(2\sqrt{6}-4\sqrt{3}\right)\sqrt{6}+12\sqrt{2}=12-12\sqrt{2}+12\sqrt{2}=12\\ b,=\dfrac{6\left(3-\sqrt{3}\right)}{6}+\sqrt{3}=3-\sqrt{3}+\sqrt{3}=3\)
1 + 6 + 11 + 16 + ... + 45 + 51
số số hạng là : ( 51 - 1 ) : 5 + 1 = 11 ( số )
tổng là : ( 51 + 1 ) x 11 : 2 = 286
làm tương tự nhé. nhiều quá làm ko nổi
1 + 2 + 3 + ... + 98 + 99 + 100
số số hạng là : ( 100 - 1 ) : 1 + 1 = 100 ( số )
tổng là : ( 100 + 1 ) x 100 : 2 = 5050
2 + 4 + 6 + ... + 98 + 100
số số hạng là : ( 100 - 2 ) : 2 + 1 = 50 số
tổng là : ( 100 + 2 ) x 50 : 2 = 2550
\(\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}\)
\(=2\times\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{96}+\dfrac{1}{192}\right)\)
\(=2\times\left(\dfrac{64+32+16+8+4+2+1}{192}\right)\)
\(=\dfrac{127}{96}\)
2/3+2/6+2/12+2/24+2/48+2/96+2/192
=2/3+1/3+1/6+1/12+1/24+1/48+1/96
=\(\dfrac{64+32+16+8+4+2+1}{96}\)
=\(\dfrac{127}{96}\)
\(1,\left(3x+2\right)\left(5-x^2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+2=0\\5-x^2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{2}{3}\\-x^2=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{2}{3}\\x=\pm\sqrt{5}\end{matrix}\right.\)
Vậy \(S=\left\{-\dfrac{2}{3};-\sqrt{5};\sqrt{5}\right\}\)
\(2,-2x-\dfrac{2}{3}\left(\dfrac{3}{4}-\dfrac{1}{8}x\right)=\left(-\dfrac{1}{2}\right)^3\)
\(\Leftrightarrow-2x-\dfrac{1}{2}+\dfrac{1}{12}x=-\dfrac{1}{8}\)
\(\Leftrightarrow-2x+\dfrac{1}{12}x=-\dfrac{1}{8}+\dfrac{1}{2}\)
\(\Leftrightarrow-\dfrac{23}{12}=\dfrac{3}{8}\)
\(\Leftrightarrow x=-\dfrac{9}{46}\)
Vậy \(S=\left\{-\dfrac{9}{46}\right\}\)
\(3,\dfrac{1}{12}:\dfrac{4}{21}=3\dfrac{1}{2}:\left(3x-2\right)\)
\(\Leftrightarrow\dfrac{1}{12}.\dfrac{21}{4}=\dfrac{7}{2}.\dfrac{1}{3x-2}\)
\(\Leftrightarrow\dfrac{7}{16}=\dfrac{7}{6x-4}\)
\(\Leftrightarrow6x-4=7:\dfrac{7}{16}\)
\(\Leftrightarrow6x-4=16\)
\(\Leftrightarrow x=\dfrac{10}{3}\)
Vậy \(S=\left\{\dfrac{10}{3}\right\}\)
\(4,\dfrac{x-1}{x+2}=\dfrac{4}{5}\left(dk:x\ne-2\right)\)
\(\Rightarrow5\left(x-1\right)=4\left(x+2\right)\)
\(\Rightarrow5x-5=4x+8\)
\(\Rightarrow x=13\left(tmdk\right)\)
Vậy \(S=\left\{13\right\}\)
\(1+2+3+...+n=\frac{n\left(n+1\right)}{2}\)
\(1+3+5+7+...+\left(2n-1\right)=n^2\)
\(2+4+6+8+...+2n=n\left(n+1\right)\)
( 1/2 + 1/6 + 1/12 + 1/30 ) : ( 1/3 + 1/6 + 1/12 + 1/ 24 + 1/48 )=(1/1.2 + 1/2.3 + 1/3.4 +1/5.6 ):(1/3.1 +1/3.2 + 1/3.4 + 1/3.8 +1/3.16)=....
\(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{30}\right):\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}\right)\)
\(=\left(\frac{12}{12}+\frac{2}{12}+\frac{1}{12}+\frac{1}{30}\right):\left(\frac{16}{16}+\frac{8}{48}+\frac{4}{48}+\frac{2}{48}+\frac{1}{48}\right)\)
\(=\left(\frac{15}{12}+\frac{1}{30}\right):\frac{31}{48}\)
\(=\left(\frac{225}{180}+\frac{6}{180}\right):\frac{31}{48}\)
\(=\frac{231}{180}:\frac{31}{48}\)
\(=\frac{231}{180}.\frac{48}{31}=\frac{231.24}{90.31}\)
\(=\frac{5544}{2790}\)nếu rút gọn được thì bạn rút gon luôn nhé
(3x -48) .6 =3^2 . 2^2 + 2^3 . 3^2 - 12
(3x-48) .6 =3^2(2^2+2^3) -12
(3x-48) .6 =3^2.12-12
(3x-48) .6 =9.12-12
(3x-48) .6 =8.12
(3x-48) .6 =96
3x-48 =96:6
3x-48=16
3x=16+48
3x=64
x=64:3
x=64/3