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\(\left(3-x\right)^3=-\dfrac{27}{64}\)
\(\left(3-x\right)^3=\left(\dfrac{-3}{4}\right)^3\)
\(=>3-x=\dfrac{-3}{4}\)
\(x=3-\dfrac{-3}{4}=\dfrac{12}{4}+\dfrac{3}{4}\)
\(x=\dfrac{15}{4}\)
________
\(\left(x-5\right)^3=\dfrac{1}{-27}\)
\(\left(x-5\right)^3=\left(\dfrac{-1}{3}\right)^3\)
\(=>x-5=\dfrac{-1}{3}\)
\(x=\dfrac{-1}{3}+5=\dfrac{-1}{3}+\dfrac{15}{3}\)
\(x=\dfrac{14}{3}\)
_____________
\(\left(x-\dfrac{1}{2}\right)^3=\dfrac{27}{8}\)
\(\left(x-\dfrac{1}{2}\right)^3=\left(\dfrac{3}{2}\right)^3\)
\(=>x-\dfrac{1}{2}=\dfrac{3}{2}\)
\(x=\dfrac{3}{2}+\dfrac{1}{2}\)
\(x=2\)
________
\(\left(2x-1\right)^2=\dfrac{1}{4}\)
\(\left(2x-1\right)^2=\left(\dfrac{1}{2}\right)^2\) hoặc \(\left(2x-1\right)^2=\left(\dfrac{-1}{2}\right)^2\)
\(=>2x-1=\dfrac{1}{2}\) \(2x-1=\dfrac{-1}{2}\)
\(2x=\dfrac{1}{2}+1=\dfrac{1}{2}+\dfrac{2}{2}\) \(2x=\dfrac{-1}{2}+1=\dfrac{-1}{2}+\dfrac{2}{2}\)
\(2x=\dfrac{3}{2}\) \(2x=\dfrac{1}{2}\)
\(x=\dfrac{3}{2}:2=\dfrac{3}{2}.\dfrac{1}{2}\) \(x=\dfrac{1}{2}:2=\dfrac{1}{2}.\dfrac{1}{2}\)
\(x=\dfrac{3}{4}\) \(x=\dfrac{1}{4}\)
____________
\(\left(2-3x\right)^2=\dfrac{9}{4}\)
\(\left(2-3x\right)^2=\left(\dfrac{3}{2}\right)^2\) hoặc \(\left(2-3x\right)^2=\left(\dfrac{-3}{2}\right)^2\)
\(=>2-3x=\dfrac{3}{2}\) \(2-3x=\dfrac{-3}{2}\)
\(3x=2-\dfrac{3}{2}=\dfrac{4}{2}-\dfrac{3}{2}\) \(3x=2-\dfrac{-3}{2}=\dfrac{4}{2}+\dfrac{3}{2}\)
\(3x=\dfrac{1}{2}\) \(3x=\dfrac{7}{2}\)
\(x=\dfrac{1}{2}.\dfrac{1}{3}\) \(x=\dfrac{7}{2}.\dfrac{1}{3}\)
\(x=\dfrac{1}{6}\) \(x=\dfrac{7}{6}\)
______________
\(\left(1-\dfrac{2}{3}\right)^2=\dfrac{4}{9}\) -> Kiểm tra đề câu này
(3-x)3=(-\(\dfrac{3}{4}\))3
3-x=-\(\dfrac{3}{4}\)
x=3-(-\(\dfrac{3}{4}\))
x=\(\dfrac{15}{4}\)
Để giải phương trình, ta sẽ thực hiện các bước sau: Bước 1: Giải các phép tính trong phương trình. 32x^(-1) + 2.9x^(-1) = 405(13)^(-1) + 5.(13)^2 + 1 = 1493(31)^(-1) + 5.(31)^2 + 1 = 9314(35)^(-1) Bước 2: Rút gọn các số hạng. 32x^(-1) + 2.9x^(-1) = 405/13 + 5.(13)^2 + 1 = 1493/31 + 5.(31)^2 + 1 = 9314/35 Bước 3: Đưa các số hạng về cùng mẫu số. 32x^(-1) + 2.9x^(-1) = (405/13).(31/31) + 5.(13)^2 + 1 = (1493/31).(13/13) + 5.(31)^2 + 1 = 9314/35 Bước 4: Tính toán các số hạng. 32x^(-1) + 2.9x^(-1) = 405.(31)/13.(31) + 5.(13)^2 + 1 = 1493.(13)/31.(13) + 5.(31)^2 + 1 = 9314/35 Bước 5: Tính tổng các số hạng. 32x^(-1) + 2.9x^(-1) = 405.(31)/403 + 5.(13)^2 + 1 = 1493.(13)/403 + 5.(31)^2 + 1 = 9314/35 Bước 6: Đưa phương trình về dạng chuẩn. 32x^(-1) + 2.9x^(-1) - 9314/35 = 0 Bước 7: Giải phương trình. Để giải phương trình này, ta cần biến đổi nó về dạng tương đương. Nhân cả hai vế của phương trình với 35 để loại bỏ mẫu số. 35.(32x^(-1) + 2.9x^(-1) - 9314/35) = 0 1120x^(-1) + 101.5x^(-1) - 9314 = 0 Bước 8: Tìm giá trị của x. Để tìm giá trị của x, ta cần giải phương trình này. Tuy nhiên, phương trình này không thể giải được vì x có mũ là -1.
\(\dfrac{8^{14}}{4^4.64^5}=\dfrac{\left(2^3\right)^{14}}{\left(2^2\right)^4.\left(2^5\right)^5}=\dfrac{2^{42}}{2^8.2^{25}}=2^{42-\left(8+25\right)}=2^9\)
\(\dfrac{9^{10}.27^7}{81^7.3^{15}}=\dfrac{\left(3^2\right)^{10}.\left(3^3\right)^7}{\left(3^4\right)^7.3^{15}}=\dfrac{3^{20}.3^{21}}{3^{28}.3^{15}}=\dfrac{3^{20+21}}{3^{28+15}}=\dfrac{3^{41}}{3^{41}.3^2}=\dfrac{1}{3^2}=\dfrac{1}{9}\)
\(a,3-x=x+1,8\)
\(\Rightarrow-x-x=1,8-3\)
\(\Rightarrow-2x=-1,2\)
\(\Rightarrow x=0,6\)
\(b,2x-5=7x+35\)
\(\Rightarrow2x-7x=35+5\)
\(\Rightarrow-5x=40\)
\(\Rightarrow x=-8\)
\(c,2\left(x+10\right)=3\left(x-6\right)\)
\(\Rightarrow2x+20=3x-18\)
\(\Rightarrow2x-3x=-18-20\)
\(\Rightarrow-x=-38\)
\(\Rightarrow x=38\)
\(d,8\left(x-\dfrac{3}{8}\right)+1=6\left(\dfrac{1}{6}+x\right)+x\)
\(\Rightarrow8x-3+1=1+6x+x\)
\(\Rightarrow8x-3=7x\)
\(\Rightarrow8x-7x=3\)
\(\Rightarrow x=3\)
\(e,\dfrac{2}{9}-3x=\dfrac{4}{3}-x\)
\(\Rightarrow-3x+x=\dfrac{4}{3}-\dfrac{2}{9}\)
\(\Rightarrow-2x=\dfrac{10}{9}\)
\(\Rightarrow x=-\dfrac{5}{9}\)
\(g,\dfrac{1}{2}x+\dfrac{5}{6}=\dfrac{3}{4}x-\dfrac{1}{2}\)
\(\Rightarrow\dfrac{1}{2}x-\dfrac{3}{4}x=-\dfrac{1}{2}-\dfrac{5}{6}\)
\(\Rightarrow-\dfrac{1}{4}x=-\dfrac{4}{3}\)
\(\Rightarrow x=\dfrac{16}{3}\)
\(h,x-4=\dfrac{5}{6}\left(6-\dfrac{6}{5}x\right)\)
\(\Rightarrow x-4=5-x\)
\(\Rightarrow x+x=5+4\)
\(\Rightarrow2x=9\)
\(\Rightarrow x=\dfrac{9}{2}\)
\(k,7x^2-11=6x^2-2\)
\(\Rightarrow7x^2-6x^2=-2+11\)
\(\Rightarrow x^2=9\Rightarrow\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)
\(m,5\left(x+3\cdot2^3\right)=10^2\)
\(\Rightarrow5\left(x+24\right)=100\)
\(\Rightarrow x+24=20\)
\(\Rightarrow x=-4\)
\(n,\dfrac{4}{9}-\left(\dfrac{1}{6^2}\right)=\dfrac{2}{3}\left(x-\dfrac{2}{3}\right)^2+\dfrac{5}{12}\)
\(\Rightarrow\dfrac{2}{3}\left(x-\dfrac{2}{3}\right)^2+\dfrac{5}{12}=\dfrac{4}{9}-\dfrac{1}{36}\)
\(\Rightarrow\dfrac{2}{3}\left(x-\dfrac{2}{3}\right)^2+\dfrac{5}{12}=\dfrac{5}{12}\)
\(\Rightarrow\dfrac{2}{3}\left(x-\dfrac{2}{3}\right)^2=0\)
\(\Rightarrow x-\dfrac{2}{3}=0\Rightarrow x=\dfrac{2}{3}\)
#\(Urushi\text{☕}\)
\(\dfrac{\left(13\dfrac{1}{4}-1\dfrac{5}{27}-10\dfrac{5}{6}\right).230\dfrac{1}{25}+46\dfrac{3}{4}}{\left(1\dfrac{3}{7}+\dfrac{10}{3}\right):\left(12\dfrac{1}{3}-14\dfrac{2}{7}\right)}\)
\(=\dfrac{1\dfrac{25}{108}.230\dfrac{1}{25}+46\dfrac{3}{4}}{4\dfrac{16}{21}:\left(-1\dfrac{20}{21}\right)}=\dfrac{330\dfrac{1}{25}}{-2\dfrac{18}{41}}=-135,3164\)
a,\(\left(\dfrac{1}{5}-\dfrac{3}{2}x\right)^2=\dfrac{9}{4}\)
\(\dfrac{1}{5}-\dfrac{3}{2}x=\dfrac{3}{2}\)
\(\dfrac{3}{2}x=-\dfrac{13}{10}\)
\(x=-\dfrac{13}{15}\)
b,\(\left(3x+1\right)^3=-27\)
\(3x+1=-3\)
\(3x=-4\)
\(x=-\dfrac{4}{3}\)
a ) \(\left(\dfrac{1}{5}-\dfrac{3}{2}x\right)^2=\dfrac{9}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{5}-\dfrac{3}{2}x=\dfrac{3}{2}\\\dfrac{1}{5}-\dfrac{3}{2}x=-\dfrac{3}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{3}{2}x=-\dfrac{13}{10}\\\dfrac{3}{2}x=\dfrac{17}{10}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{13}{15}\\x=\dfrac{17}{15}\end{matrix}\right.\)
Vậy .......
b ) \(\left(3x+1\right)^3=-27\)
\(\Leftrightarrow3x+1=-3\)
\(\Leftrightarrow3x=-4\Leftrightarrow x=-\dfrac{4}{3}\)
Vậy ..........
c ) \(7.3^{x-1}-3^{x+2}=-540\)
\(\Leftrightarrow7.3^{x-1}-3^{x-1}.3^3=-540\)
\(\Leftrightarrow3^{x-1}\left(7-27\right)=-540\)
\(\Leftrightarrow-20.3^{x-1}=-540\)
\(\Leftrightarrow3^{x-1}=27\)
\(\Leftrightarrow x=4\).
Vậy ..........
a, Theo đề ta có:
\(2.3^x-405=3^{x-1}\)
=> \(2.3^x-405=3^x:3\)
=> \(405=(2.3^x)-(3^x:3)\)
=>\(405=(2.3^x)-(3^x.\dfrac{1}{3})\)
=> \(405=3^x(2-\dfrac{1}{3})\)
=>\(405=3^x(\dfrac{6}{3}-\dfrac{1}{3})\)
=> \(405=3^x.\dfrac{5}{3}\)
=> \(3^x=405:\dfrac{5}{3}\)
=>\(3^x=405.\dfrac{3}{5}\)
=> \(3^x=81.3\)
=> \(3^x=243\)
=> \(3^x=3^5\)
=> x=5
Vậy:..............................
1. \(\left(-\dfrac{3}{2}\right)^2=\dfrac{9}{4}\)
\(\Rightarrow\left(-\dfrac{3}{2}\right)^x=\left(-\dfrac{3}{2}\right)^2\)
\(\Rightarrow x=2\)
2.\(3^{2x+2}=9^{10}\)
\(\Rightarrow3^{2x+2}=\left(3^2\right)^{10}\)
\(\Rightarrow3^{2x+2}=3^{20}\)
\(\Rightarrow2x+2=20\)
\(\Rightarrow2x=18\)
\(\Rightarrow x=9\)
3)\(3^{3-2x}=27^{13}\)
\(\Rightarrow3^{3-2x}=\left(3^3\right)^{13}\)
\(\Rightarrow3^{3-2x}=3^{39}\)
\(\Rightarrow3-2x=39\)
\(\Rightarrow2x=-36\)
\(\Rightarrow x=-18\)
4)\(5.3^x=7.3^5-2.3^5\)
\(\Rightarrow5.3^x=3^5\left(7-2\right)\)
\(\Rightarrow5.3^x=3^5.5\)
\(\Rightarrow3^x=3^5\)
\(\Rightarrow x=5\)