\(2^4.x-3.5x=5^2-2^4\)

\(x\left(16-15\right)=25-16\)

\(x=9\)

\(\dfrac{2^2}{1\times3}\times\dfrac{3^2}{2.4}\times\dfrac{4^2}{3.5}\times\dfrac{5^2}{4.6}=\dfrac{2^2.3^2.4^2.5^2}{1.3.2.4.3.5.4.6}=\dfrac{2^2.3^2.4^2.5^2}{1.2.3.3.4.4.5.2.3}=\dfrac{2^2.3^2.4^2.5^2}{3^3.2^2.4^2.5.1}=\dfrac{5}{3.1}=\dfrac{5}{3}\)

\(\dfrac{2^2}{1\cdot3}\cdot\dfrac{3^2}{2\cdot4}\cdot\dfrac{4^2}{3\cdot5}\cdot\dfrac{5^2}{4.6}\\ =\dfrac{2^2\cdot3^2\cdot4^2\cdot5^2}{1\cdot3\cdot2\cdot4\cdot3\cdot5\cdot4\cdot6}\\ =\dfrac{2^2\cdot3^2\cdot4^2\cdot5^2}{1\cdot2\cdot4^2\cdot4^2\cdot5\cdot6}\\ =\dfrac{2\cdot5}{6}=\dfrac{5}{3}\)

\(\text{a.61 x 23 + 39 x 22}\)

\(=61.22+1+39.22\)

\(=22.\left(61+39\right)+1\)

\(=22.100+1\)

\(=2200+1\)

\(=2201\)

mình chỉ làm được 1 câu thôi

hok tốt

61*23+39*22

=(61+39)*22+61

=100*22+61

=2200+61

=2261

61 x 23 + 39 x 22 = 61 x ( 22 + 1 ) + 39 x 22 = 61 x 22 + 61 + 39 x 22 = 22 x ( 61 + 39 ) + 61 = 22 x 100 + 61 = 2 200 +61 = 2 261

a) \(\frac{x}{24}=\frac{6}{x}\)

\(\Leftrightarrow x^2=24.6\)

\(\Leftrightarrow x^2=144\)

\(\Leftrightarrow x=12\)

\(\frac{x}{24}=\frac{6}{x}\)

\(\Leftrightarrow x.x=6.24\)

\(\Leftrightarrow x^2=6.24\)

\(\Leftrightarrow x^2=144\)

\(\Leftrightarrow x=\pm12\)

1) Tìm x biết : 

a) \(\frac{x}{24}=\frac{6}{x}\)

\(\Leftrightarrow x.x=24.6\)

\(\Rightarrow x^2=144\)

\(\Rightarrow x^2=12^2\)

\(\Rightarrow x=\pm12\)

b) \(2x+\frac{3}{24}=3x-\frac{1}{32}\)

\(\Rightarrow2x-3x=-\frac{3}{24}-\frac{1}{32}\)

\(\Rightarrow-x=-\frac{5}{32}\)

\(\Rightarrow x=\frac{5}{32}\)

thầy nhật có biết ko t

\(1+5^2+5^4+...+5^{2x}\left(1\right)=\dfrac{25^6-1}{24}\)

Đặt \(\left(1\right)=A\)

\(\Rightarrow A=1+5^2+...+5^{2x}\)

\(\Rightarrow5^2A=5^2+5^4+...+5^{2x+2}\)

\(\Rightarrow25A=5^2+5^4+...+5^{2x+2}\)

\(\Rightarrow25A-A=5^2+5^4+...+5^{2x+2}-1-5^2-...-5^{2x}\)

\(\Rightarrow24A=5^{2x+2}-1\)

\(\Rightarrow A=\dfrac{5^{2x+2}-1}{24}\)

Mà: \(A=\dfrac{25^6-1}{24}\)

\(\Rightarrow\dfrac{5^{2x+2}-1}{24}=\dfrac{\left(5^2\right)^6-1}{24}\)

\(\Rightarrow5^{2x+2}-1=5^{12}-1\)

\(\Rightarrow5^{2x+2}=5^{12}\)

\(\Rightarrow2x+2=12\)

\(\Rightarrow2x=10\)

\(\Rightarrow x=\dfrac{10}{2}\)

\(\Rightarrow x=5\)