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a) Tìm giá trị của x để biểu thức A=|x-0,25| có giá trị nhỏ nhất.
TA Có : \(A=\text{|x-0,25|}\ge0\)
\(\Rightarrow Amin=0\)
\(\Rightarrow\text{x-0,25=0}\)
\(\Rightarrow x=0,25\)
Vậy A min khi x=0,25
a) \(2,5:2,7=x:\frac{3}{5}\)
\(\Rightarrow\frac{5}{2}:\frac{27}{10}=x.\frac{5}{3}\)
\(\Rightarrow\frac{5}{2}.\frac{10}{27}=\frac{5x}{3}\)
\(\Rightarrow\frac{25}{27}=\frac{5x}{3}\)
\(\Rightarrow5x=\frac{25.3}{27}=\frac{75}{27}=\frac{25}{9}\)
\(\Rightarrow x=\frac{25}{9}:5=\frac{25}{9}.\frac{1}{5}=\frac{5}{9}\)
b) \(\frac{19}{5}:\frac{608}{15}=0,25:x\)
\(\Rightarrow\frac{19}{5}.\frac{15}{608}=\frac{1}{4}:x\)
\(\Rightarrow\frac{3}{32}=\frac{1}{4}:x\)
\(\Rightarrow x=\frac{1}{4}:\frac{3}{32}=\frac{1}{4}.\frac{32}{3}=\frac{8}{3}\)
c/ \(\frac{8}{3}:x=\frac{16}{9}:0,2\)
\(\Rightarrow\frac{8}{3}:x=\frac{16}{9}:\frac{1}{5}=\frac{16}{9}.5=\frac{80}{9}\)
\(\Rightarrow x=\frac{8}{3}:\frac{80}{9}=\frac{8}{3}.\frac{9}{80}=\frac{3}{10}\)
\(=\dfrac{11}{4}:\dfrac{33}{16}-0,5+\left(\dfrac{14}{5}-3\right)^2\\ =\dfrac{11}{4}\cdot\dfrac{16}{33}-\dfrac{1}{2}+\left(-\dfrac{1}{5}\right)^2\\ =\dfrac{4}{3}-\dfrac{1}{2}+\dfrac{1}{25}=\dfrac{131}{150}\)
1)
a. \(\left(3x^2-50\right)^2=5^4\)
\(\Leftrightarrow3x^4-50=625\)
\(\Leftrightarrow3x^4=675\)
\(\Leftrightarrow x^4=225\)
\(\Leftrightarrow x=\sqrt{15}\)
2)
a. \(\frac{\left(3^4-3^3\right)^4}{27^3}=\frac{3^{16}-3^{12}}{\left(3^3\right)^3}=\frac{3^{12}.3^4-3^{12}}{3^9}=\frac{3^{12}\left(3^4-1\right)}{3^9}\)
\(=\frac{3^{12}.80}{3^9}=3^3.80=27.80=2160\)
b. \(\frac{25^3}{\left(5^5-5^3\right)^2}=\frac{\left(5^2\right)^3}{5^{10}-5^6}=\frac{5^6}{5^6.5^4-5^6}=\frac{5^6}{5^6\left(5^4-1\right)}\)
\(=\frac{5^6}{5^6.624}=\frac{1}{624}\)
\(\left(\frac{3}{7}\right)^{20}:\left(\frac{9}{49}\right)^5\)
\(=\left(\frac{3}{7}\right)^{20}:\left(\frac{3^2}{7^2}\right)^5\)
\(=\left(\frac{3}{7}\right)^{20}:\left(\frac{3}{7}\right)^{10}\)
\(=\left(\frac{3}{7}\right)^{10}\)
\(2:\left(\frac{1}{2}-\frac{2}{3}\right)^2\)
\(=2:\left(\frac{3}{6}-\frac{4}{6}\right)^2\)
\(=2:\left(\frac{-1}{6}\right)^2\)
\(=2:\frac{1}{36}=2.36\)
\(=72\)
\(\sqrt{16}+\sqrt{0,25}-\sqrt{0,36}\)
\(=4+0,5-0,6\)
\(=3,9\)
\(\dfrac{6}{5}\sqrt{1\dfrac{9}{16}}-\left(-\dfrac{3}{4}\right)^2:0,25\)
\(=\dfrac{6}{5}\cdot\sqrt{\dfrac{25}{16}}-\dfrac{9}{16}:0,25\)
\(=\dfrac{6}{5}\cdot\sqrt{\left(\dfrac{5}{4}\right)^2}-\dfrac{9}{16}:\dfrac{1}{4}\)
\(=\dfrac{6}{5}\cdot\dfrac{5}{4}-\dfrac{9\cdot4}{16}\)
\(=\dfrac{6}{4}-\dfrac{9}{4}\)
\(=\dfrac{6-9}{4}\)
\(=-\dfrac{3}{4}\)
\(\dfrac{6}{5}\cdot\sqrt{\dfrac{25}{16}}-\left(\dfrac{3}{4}\right)^2:0,25\\ =\dfrac{6}{5}\cdot\dfrac{5}{4}-\dfrac{9}{16}\cdot4\\ =\dfrac{3}{2}-\dfrac{9}{4}\\ =-\dfrac{3}{4}\)
\(\dfrac{6}{5}\cdot\sqrt{\dfrac{25}{16}}-\left(\dfrac{3}{4}\right)^2:0,25\)
\(=\dfrac{6}{5}\cdot\dfrac{5}{4}-\dfrac{9}{16}:\dfrac{1}{4}\)
\(=\dfrac{6\cdot5}{5\cdot4}-\dfrac{9\cdot4}{16}\)
\(=\dfrac{6}{4}-\dfrac{9}{4}\)
\(=\dfrac{3}{4}\)