?????????????????

a) \(x=2\)

b) \(x=\frac{5}{36}\)

a) \(1-\left(\frac{2x}{3}+2\right)=-1\cdot\frac{1}{3}\)

\(1-\frac{2}{3}x-2=-\frac{1}{3}\)

\(-\frac{2}{3}x-1=-\frac{1}{3}\)

\(-\frac{2}{3}x=\frac{2}{3}\)

\(x=-1\)

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b) \(\frac{2}{5}x-1\cdot\frac{1}{2}x+x=\frac{1}{3}\)

\(\left(\frac{2}{5}-\frac{1}{2}+1\right)x=\frac{1}{3}\)

\(\frac{9}{10}x=\frac{1}{3}\)

\(x=\frac{1}{3}:\frac{9}{10}\)

\(x=\frac{10}{27}\)

1: \(\dfrac{1}{3-2\sqrt{2}}+\dfrac{1}{\sqrt{5}+2}\)

\(=\dfrac{3+2\sqrt{2}}{1}+\dfrac{\sqrt{5}-2}{1}\)

\(=3+2\sqrt{2}+\sqrt{5}-2=2\sqrt{2}+\sqrt{5}+1\)

2: \(\dfrac{1}{\sqrt{3}+\sqrt{7}}+\dfrac{2}{1-\sqrt{7}}\)

\(=\dfrac{\sqrt{7}-\sqrt{3}}{4}+\dfrac{2\left(1+\sqrt{7}\right)}{-6}\)

\(=\dfrac{\sqrt{7}-\sqrt{3}}{4}-\dfrac{1+\sqrt{7}}{3}\)

\(=\dfrac{3\left(\sqrt{7}-\sqrt{3}\right)-4\left(\sqrt{7}+1\right)}{12}=\dfrac{-\sqrt{7}-3\sqrt{3}-4}{12}\)

3:

\(=\dfrac{\sqrt{a}\left(\sqrt{a}-2\right)}{2-\sqrt{a}}=-\dfrac{\sqrt{a}\left(\sqrt{a}-2\right)}{\sqrt{a}-2}=-\sqrt{a}\)

4:

\(=\dfrac{\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}+\sqrt{y}}\)

\(=\sqrt{xy}\)

1) \(\dfrac{1}{3-2\sqrt{2}}+\dfrac{1}{\sqrt{5}+2}\)

\(=\dfrac{3+2\sqrt{2}}{\left(3-2\sqrt{2}\right)\left(3+2\sqrt{2}\right)}+\dfrac{\sqrt{5}-2}{\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)}\)

\(=\dfrac{3+2\sqrt{2}}{3^2-\left(2\sqrt{2}\right)^2}+\dfrac{\sqrt{5}-2}{\left(\sqrt{5}\right)^2-2^2}\)

\(=\dfrac{3+2\sqrt{2}}{1}+\dfrac{\sqrt{5}-2}{1}\)

\(=3+2\sqrt{2}+\sqrt{5}-2\)

\(=2\sqrt{2}+\sqrt{5}+1\)

2) \(\dfrac{1}{\sqrt{3}-\sqrt{7}}+\dfrac{2}{1-\sqrt{7}}\)

\(=\dfrac{\sqrt{3}+\sqrt{7}}{\left(\sqrt{3}+\sqrt{7}\right)\left(\sqrt{3}-\sqrt{7}\right)}+\dfrac{2\cdot\left(1+\sqrt{7}\right)}{\left(1-\sqrt{7}\right)\left(1+\sqrt{7}\right)}\)

\(=\dfrac{\sqrt{3}+\sqrt{7}}{\left(\sqrt{3}\right)^2-\left(\sqrt{7}\right)^2}+\dfrac{2\cdot\left(1+\sqrt{7}\right)}{1^2-\left(\sqrt{7}\right)^2}\)

\(=\dfrac{-\sqrt{3}-\sqrt{7}}{4}-\dfrac{2\cdot\left(1+\sqrt{7}\right)}{6}\)

\(=\dfrac{-\sqrt{3}-\sqrt{7}}{4}-\dfrac{1+\sqrt{7}}{3}\)

\(=\dfrac{-3\sqrt{3}-3\sqrt{7}}{12}-\dfrac{4+4\sqrt{7}}{12}\)

\(=\dfrac{-3\sqrt{3}-3\sqrt{7}-4-4\sqrt{7}}{12}\)

\(=\dfrac{-3\sqrt{3}-7\sqrt{7}-4}{12}\)

3) \(\dfrac{a-2\sqrt{a}}{2-\sqrt{a}}\)

\(=-\dfrac{a-2\sqrt{a}}{\sqrt{a}-2}\)

\(=-\dfrac{\sqrt{a}\cdot\left(\sqrt{a}-2\right)}{\sqrt{a}-2}\)

\(=-\sqrt{a}\)

4) \(\dfrac{x\sqrt{y}+y\sqrt{x}}{\sqrt{x}+\sqrt{y}}\)

\(=\dfrac{\sqrt{x}\cdot\sqrt{xy}+\sqrt{y}\cdot\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\)

\(=\dfrac{\sqrt{xy}\cdot\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}+\sqrt{y}}\)

\(=\sqrt{xy}\)

Ta có:

 S = 1.1!+2.2!+3.3!+.....+100.100!

 S = (1+1-1).1!+(2+1-1).2!+...+(100+1-1).100!

 S = 2!-1+3!-2!+4!-3!+...+101!-100!

 S = 101!+(100!-100!)+(99!-99!)+...+(2!-2!)-1

 S = 101!-1

k cho mk nha bạn 

                       S=101! - 1

1.1

a, GTNN của A = 10 <=> x=-3

b, GTNN của B = -7 <=> x = -1

1.2

a,GTLN của C = -3 <=> x = 2

b, GTLN của D = 15 <=> x = 4

k mk nha