toán này của lố 1 chết tại chỗ!!! >:(
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\(\sqrt{10+\sqrt{24}-\sqrt{60}-\sqrt{40}}\)
\(=\sqrt{\sqrt{2}^2+\sqrt{3}^2+\left(-\sqrt{5}\right)^2+2\sqrt{2.3}-2\sqrt{2.5}-2\sqrt{3.5}}\)
\(=\sqrt{\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right)^2}\)
\(=\sqrt{2}+\sqrt{3}-\sqrt{5}\)
Tìm x là số nguyên dương
\(\sqrt{\left(5-2\sqrt{6}\right)^x}+\sqrt{\left(5+2\sqrt{6}\right)^x}=10\)
b, MA-Bfrac{sqrt{x}+2}{sqrt{x}+3}-left(frac{5}{x+sqrt{x}-6}+frac{1}{sqrt{x}-2}right)frac{sqrt{x}+2}{sqrt{x}+3}-frac{5}{x+sqrt{x}-6}-frac{1}{sqrt{x}-2}frac{left(sqrt{x}+2right)left(sqrt{x}-2right)}{x+sqrt{x}-6}-frac{5}{x+sqrt{x}-6}-frac{1left(sqrt{x}+3right)}{x+sqrt{x}-6}frac{x-4-5-sqrt{x}-3}{left(sqrt{x}+3right)left(sqrt{x}-2right)}frac{x-sqrt{x}-12}{left(sqrt{x}+3right)left(sqrt{x}-2right)}frac{x-4sqrt{x}+3sqrt{x}-12}{left(sqrt{x}+3right)left(sqrt{x}-2right)}frac{left(sqrt{x}-4right)left(sqrt{x...
Đọc tiếp
b, \(M=A-B=\frac{\sqrt{x}+2}{\sqrt{x}+3}-\left(\frac{5}{x+\sqrt{x}-6}+\frac{1}{\sqrt{x}-2}\right)\)
\(=\frac{\sqrt{x}+2}{\sqrt{x}+3}-\frac{5}{x+\sqrt{x}-6}-\frac{1}{\sqrt{x}-2}\)
\(=\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}{x+\sqrt{x}-6}-\frac{5}{x+\sqrt{x}-6}-\frac{1\left(\sqrt{x}+3\right)}{x+\sqrt{x}-6}\)
\(=\frac{x-4-5-\sqrt{x}-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}=\frac{x-\sqrt{x}-12}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}=\frac{x-4\sqrt{x}+3\sqrt{x}-12}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)\(=\frac{\left(\sqrt{x}-4\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+3\right)}=\frac{\sqrt{x}-4}{\sqrt{x}-2}\)
\(B=x-4\sqrt{x}+\frac{x+16}{\sqrt{x}+3}+10=x-4\sqrt{x}+4+\frac{4\left(\sqrt{x}+3\right)+x-4\sqrt{x}+4}{\sqrt{x}+3}+6\)
\(=\left(\sqrt{x}-2\right)^2+\frac{\left(\sqrt{x}-2\right)^2}{\sqrt{x}+3}+4+6\ge10\)Dấu = xảy ra tại x=4
:(sqrt( cos( x))* cos( 300* x)+ sqrt( abs( x))- 0.7)* (4- x* x)^ 0.01* sqrt( 6- x^ 2)- sqrt( 6- x^ 2)
Tính: \(1+1\frac{3}{4}+\frac{6}{5}-5+12,4=?\)
\(5+4+\sqrt{100}-\sqrt{25}+12,5=?\)
\(A=\frac{2-5\sqrt{x}}{\sqrt{x}+3}=\frac{17-5\left(\sqrt{x}+3\right)}{\sqrt{x}+3}=\frac{17}{\sqrt{x}+3}-5\)
Vì \(\sqrt{x}+3\ge3\)(Mọi \(x\ge0\)) \(\Rightarrow A\le\frac{17}{3}-5=\frac{2}{3}\)
Dấu = xảy ra khi x=0 (t/m)
À bạn thêm cái đk của x lên đầu là \(x\ge0\) nhé
GL.
D frac{x^2-2x+2000}{x^2} 1-frac{2x}{x^2}+frac{2000}{x^2}Đặt t frac{1}{2} D 2000t2-2t+1 (20sqrt{5}t)2-2.20sqrt{5}t.frac{1}{20sqrt{5}}+left(frac{1}{20sqrt{5}}right)^2-left(frac{1}{20sqrt{5}}right)^2+1D (20sqrt{5}t-frac{1}{20sqrt{5}}) 2+frac{1999}{2000}gefrac{1999}{2000}Min D frac{1999}{2000}khi 20sqrt{5}t-frac{1}{20sqrt{5}} 0 t frac{1}{2000} frac{1}{x} frac{1}{2000} x 2000
Đọc tiếp
D= \(\frac{x^2-2x+2000}{x^2}\)= 1-\(\frac{2x}{x^2}\)+\(\frac{2000}{x^2}\)
Đặt t= \(\frac{1}{2}\)=> D= 2000t2-2t+1 = (\(20\sqrt{5}t\))2-2.\(20\sqrt{5}t\).\(\frac{1}{20\sqrt{5}}\)+\(\left(\frac{1}{20\sqrt{5}}\right)^2\)\(-\left(\frac{1}{20\sqrt{5}}\right)^2\)+1
D= (\(20\sqrt{5}t\)-\(\frac{1}{20\sqrt{5}}\)) 2+\(\frac{1999}{2000}\)\(\ge\)\(\frac{1999}{2000}\)
Min D= \(\frac{1999}{2000}\)khi \(20\sqrt{5}t\)\(-\frac{1}{20\sqrt{5}}\)= 0 => t = \(\frac{1}{2000}\)=> \(\frac{1}{x}\)= \(\frac{1}{2000}\)=> x= 2000
\(\sqrt{\sqrt[2]{3}\sqrt[2]{5}\frac{\left(\int^2_7^3\right)}{1234}}\)