\(=\dfrac{10\cdot11+25\cdot10\cdot11+49\cdot10\cdot11}{11\cdot12+25\cdot11\cdot12+49\cdot11\cdot12}=\dfrac{10\cdot11}{11\cdot12}=\dfrac{10}{12}=\dfrac{5}{6}\)

5/6

có : n+2/n+3 - n+1/n+2= ((n+2) x (n+2) -  (n+1) x (n+3))/(n+2)x(n+3)=1/(n+2)x(n+3) > 0

suy ra n+1/n+2 < n+2/ n+3

ví dụ: 1/2 < 2/3

\(\sqrt{7-\sqrt{24}}-\dfrac{\sqrt{50}-5}{\sqrt{10}-\sqrt{5}}+\sqrt{\left(11+\sqrt{120}\right)\left(11+2\sqrt{30}\right)^2}\)

\(=\sqrt{7-2\sqrt{6}}-\dfrac{5\left(\sqrt{2}-1\right)}{\sqrt{5}\left(\sqrt{2}-1\right)}+\left|11+2\sqrt{30}\right|\sqrt{11-2\sqrt{30}}\)

\(=\sqrt{1^2-2\sqrt{6}\cdot1+\left(\sqrt{6}\right)^2}-\dfrac{\sqrt{5}\cdot\sqrt{5}}{\sqrt{5}}+\left(11+2\sqrt{30}\right)\sqrt{\left(\sqrt{6}\right)^2-2\sqrt{5}\cdot\sqrt{6}+\left(\sqrt{5}\right)^2}\)

\(=\sqrt{\left(1-\sqrt{6}\right)^2}-\sqrt{5}+\left(11+2\sqrt{30}\right)\sqrt{\left(\sqrt{6}-\sqrt{5}\right)^2}\)

\(=\left|1-\sqrt{6}\right|-\sqrt{5}+\left(11+2\sqrt{30}\right)\left|\sqrt{6}-\sqrt{5}\right|\)

\(=-1+6-\sqrt{5}+\left(\sqrt{6}+\sqrt{5}\right)^2\left(\sqrt{6}-\sqrt{5}\right)\)

\(=\sqrt{6}-1-\sqrt{5}+\left[\left(\sqrt{6}\right)^2-\left(\sqrt{5}\right)^2\right]\left(\sqrt{6}+\sqrt{5}\right)\)

\(=\sqrt{6}-1-\sqrt{5}+\left(6-5\right)\left(\sqrt{6}+\sqrt{5}\right)\)

\(=\sqrt{6}-1-\sqrt{5}+\sqrt{6}+\sqrt{5}\)

\(=2\sqrt{6}-1\)

\(=\sqrt{6+1-2\sqrt{6}}-\dfrac{\sqrt{5}\left(\sqrt{10}-\sqrt{5}\right)}{\sqrt{10}-\sqrt{5}}+\sqrt{\left(11-\sqrt{120}\right)\left(11+\sqrt{120}\right)^2}\\ =\sqrt{\left(\sqrt{6}-\sqrt{1}\right)^2}-\sqrt{5}+\sqrt{\left(11^2-120\right)\left(11+2\sqrt{30}\right)}\\ =\sqrt{6}-\sqrt{1}-\sqrt{5}+\sqrt{1\left(6+5+2\sqrt{6\cdot5}\right)}\\ =\sqrt{6}-\sqrt{1}-\sqrt{5}+\sqrt{\left(\sqrt{6}+\sqrt{5}\right)^2}\\ =\sqrt{6}-\sqrt{1}-\sqrt{5}+\sqrt{6}+\sqrt{5}=2\sqrt{6}-\sqrt{1}\)

a)

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

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

b)

\(\left(2+\dfrac{11-\sqrt{11}}{1-\sqrt{11}}\right)\left(2+\dfrac{\sqrt{11}+11}{\sqrt{11}+1}\right)\\ =\left(2+\dfrac{\sqrt{11}\left(\sqrt{11}-1\right)}{-\left(\sqrt{11}-1\right)}\right)\left(2+\dfrac{\sqrt{11}\left(1+\sqrt{11}\right)}{\sqrt{11}+1}\right)\\ =\left(2-\sqrt{11}\right)\left(2+\sqrt{11}\right)\\ =4-11\\ =-7\)

a: \(=\left(\dfrac{\sqrt{3}\left(2+\sqrt{3}\right)}{2+\sqrt{3}}-\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}\right)\left(\sqrt{3}+\sqrt{2}\right)\)

=(căn 3-căn 2)(căn 3+căn 2)

=3-2=1

b: \(=\left(2-\dfrac{\sqrt{11}\left(\sqrt{11}-1\right)}{\sqrt{11}-1}\right)\left(2+\dfrac{\sqrt{11}\left(\sqrt{11}+1\right)}{\sqrt{11}+1}\right)\)

=(2-căn 11)(2+căn 11)

=4-11

=-7

\(\dfrac{50}{60}=\dfrac{5}{6}\)
\(\dfrac{33}{11}=3\)
\(\dfrac{16}{60}=\dfrac{4}{15}\)
\(\dfrac{42}{22}=\dfrac{21}{11}\)

chia là gì z

50/60=5/6

33/11=3

16/60=4/15

42/22=21/11

HT ☘

1/3 + 1/5 - 1/4 = 17/60

7/8 - (1/4 + 2/5) = 9/40

5/11 - (3/5 - 6/11) = 2/5

17/60
9/40
2/5

a) \(\dfrac{1}{3}+\dfrac{1}{5}-\dfrac{1}{4}=\dfrac{20}{60}+\dfrac{12}{60}-\dfrac{15}{60}=\dfrac{32}{60}-\dfrac{15}{60}=\dfrac{17}{60}\)

b) \(\dfrac{7}{8}-\left(\dfrac{1}{4}+\dfrac{2}{5}\right)=\dfrac{7}{8}-\left(\dfrac{5}{20}+\dfrac{8}{20}\right)=\dfrac{7}{8}-\dfrac{13}{20}=\dfrac{35}{40}-\dfrac{26}{40}=\dfrac{9}{40}\)

c) \(\dfrac{5}{11}-\left(\dfrac{3}{5}-\dfrac{6}{11}\right)=\dfrac{5}{11}-\left(\dfrac{33}{55}-\dfrac{30}{55}\right)=\dfrac{5}{11}-\dfrac{3}{55}=\dfrac{25}{55}-\dfrac{3}{55}=\dfrac{22}{55}=\dfrac{2}{5}\)

xin lỗi mình mới lớp 7 thôi hihi

thôi bạn cứ k cho mink nha thank kiu

A=9×11×(11² +1)×(11⁴ +1)×(11⁸ +1)

= 9 . 11 (  11⁶ + 11² + 11⁴ + 1 )  ( 11⁸ + 1)

= 9 . 11 ( 11¹⁴+ 11⁶+ 11¹⁰+ 11² 11¹²+11⁴+ 1)

Ý kiến riêng ko chắc , bạn nên nhờ thầy cô để có kết quả chính xác hơn 

Hok tốt

B= 3¹¹+3¹²+3¹³+...+3¹⁰¹

=>3B= 3¹²+3¹³+3¹⁴+...+3¹⁰¹

=>3B-B= 3¹²+3¹³+3^14+...+3¹⁰¹-3¹¹ -3¹²-3¹³-...-3¹⁰¹

=>2B=3¹⁰¹-3¹¹

=>B= 2¹⁰¹-3¹¹ :2

A=9×11×(11² +1)×(11⁴ +1)×(11⁸ +1)

= 9 . 11 (  11⁶ + 11² + 11⁴ + 1 )  ( 11⁸ + 1)

= 9 . 11 ( 11¹⁴+ 11⁶+ 11¹⁰+ 11² 11¹²+11⁴+ 1)

Hơi tắt , ý kiến riêng , bạn nên nhờ thầy cô để có kết quả chuẩn xác hơn nha

Hok tốt

A= 99/120 x(11^2 -1)x(11^2 +1)x(11^4 +1)(11^8 +1) (11^2 -1 =120)

=99/120 x(11^4 -1)(11^4 +1)(11^8 +1)

=99/120 x(11^8 -1)(11^8 +1)

=99/120 x(11^16 -1)

Không nên tính kết quả cụ thể. Chúc bạn học tốt