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Bài 3:
a: Ta có: \(4x\left(x+1\right)=8\left(x+1\right)\)
\(\Leftrightarrow\left(x+1\right)\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)
b: Ta có: \(x\left(x-1\right)+2\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)
c: Ta có: \(2x\left(x-2\right)-\left(x-2\right)^2=0\)
\(\Leftrightarrow\left(x-2\right)\left(2x-x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
Bài 4:
\(a,\sqrt{64.\left(x-1\right)^2}=16\\ \Leftrightarrow8\sqrt{\left(x-1\right)^2}=16\\ \\ \Leftrightarrow\sqrt{\left(x-1\right)^2}=\dfrac{16}{8}=2\\ \left|x-1\right|=2\\ \Leftrightarrow\left[{}\begin{matrix}x-1=2\\x-1=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\\ b,\sqrt{4\left(x-2\right)}=8\\ \Leftrightarrow2\sqrt{x-2}=8\\ \Leftrightarrow\sqrt{x-2}=\dfrac{8}{2}=4\\ \Leftrightarrow x-2=4^2=16\\ \Leftrightarrow x=16+2=18\\ c,\dfrac{\sqrt{2x}}{\sqrt{8}}=5\\ \Leftrightarrow\dfrac{\sqrt{2}\sqrt{x}}{2\sqrt{2}}=5\\ \Leftrightarrow\dfrac{\sqrt{x}}{2}=5\\ \Leftrightarrow\sqrt{x}=5.2=10\\ \Leftrightarrow x=10^2=100\)
Bài 2:
\(a,\left(\sqrt{75}-2\sqrt{12}-\sqrt{27}\right).\sqrt{3}\\ =\left(\sqrt{3.5^2}-2.\sqrt{3.2^2}-\sqrt{3.3^2}\right).\sqrt{3}\\ =\left(5\sqrt{3}-2.2\sqrt{3}-3\sqrt{3}\right).\sqrt{3}\\ =-2\sqrt{3}.\sqrt{3}=-2.3=-6\\ b,\left(5\sqrt{2}-\sqrt{8}-\sqrt{98}\right):\sqrt{2}\\ =\left(5\sqrt{2}-\sqrt{2^2.2}-\sqrt{2.7^2}\right):\sqrt{2}\\ =\left(5\sqrt{2}-2\sqrt{2}-7\sqrt{2}\right):\sqrt{2}\\ =-4\sqrt{2}:\sqrt{2}=-4\)
\(c,\\ \dfrac{\sqrt{18}}{\sqrt{2}}=\sqrt{\dfrac{18}{2}}=\sqrt{9}=\sqrt{3^2}=3\\ d,\\ \sqrt{\dfrac{45}{7}}.\sqrt{\dfrac{28}{5}}=\sqrt{\dfrac{45.28}{7.5}}=\sqrt{\dfrac{9.5.4.7}{7.5}}=\sqrt{9.4}=\sqrt{36}=\sqrt{6^2}=6\)
Tham khảo:
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Câu 2)
b, Công thực hiện là
\(A=P.h=10m.h=10.6.12=720J\)
a, Phụ thuộc vào khối lượng và quãng đường vật di chuyển
A = F.s
A : công cần tính ( đơn vị J(Jun) ; 1kJ (ki lô jun)= 1000J)
F : lực vật tác động
s : quãng đường vật di chuyển
Câu 3)
Để tính công thực hiện trong 1s
P = A/t
P : công suất ( đơn vị W (oát) -1MGW = 1000kW = 1,000,000W)
A : công
t : thời gian (đơn vị giây)
b, Công suất thực hiện là
\(P=\dfrac{A}{t}=\dfrac{P.h}{t}=\dfrac{10m.h}{t}\\ =\dfrac{10.50.8}{50}=80W\)
Câu 4)
5p = 300s
10p = 600s
Công suất leo của Hương là
\(P=\dfrac{A}{t}=\dfrac{P.h}{t}\\ =\dfrac{10m.h}{t}=\dfrac{10.40.6}{300}=8W\)
Công suất leo của Lan là
\(P=\dfrac{10m.h}{t}=\dfrac{10.50.9}{600}=7,5W\)
Hương leo khoẻ hơn do 8 W > 7,5 W
a: A=căn x-1
=>\(\left(\sqrt{x}-1\right)\cdot\dfrac{\sqrt{x}}{3}-\left(\sqrt{x}-1\right)=0\)
=>(căn x-1)(1/3*căn x-1)=0
=>x=1 hoặc x=9
b: \(B=\dfrac{x+2\sqrt{x}+4-x+\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}\)
\(=\dfrac{3\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}=\dfrac{3}{x-\sqrt{x}+1}\)
c: \(A\cdot B< =\dfrac{\sqrt{x}-1}{x-\sqrt{x}+1}\)
=>\(\dfrac{3\left(x-\sqrt{x}\right)}{3\left(x-\sqrt{x}+1\right)}< =\dfrac{\sqrt{x}-1}{x-\sqrt{x}+1}\)
=>x-2căn x+1<=0
=>(căn x-1)^2<=0
=>x=1