\(x=\sqrt[3]{9+4\sqrt{5}}+\sqrt[3]{9-4\sqrt{5}}\)

\(\Rightarrow x^3=9+4\sqrt{5}+9-4\sqrt{5}+3\sqrt[3]{\left(9+4\sqrt[]{5}\right)\left(9-4\sqrt{5}\right)}\left(\sqrt[3]{9+4\sqrt{5}}+\sqrt[3]{9-4\sqrt{5}}\right)\)

\(=18+3\sqrt{81-80}.x=18+3x\)\(\Rightarrow x^3-3x=18\left(1\right)\)

\(y=\sqrt[3]{3+2\sqrt{2}}+\sqrt[3]{3-2\sqrt{2}}\)

\(\Rightarrow y^3=3+2\sqrt{2}+3-2\sqrt{2}+3\sqrt[3]{\left(3+2\sqrt{2}\right)\left(3-2\sqrt{2}\right)}\left(\sqrt[3]{3+2\sqrt{2}}+\sqrt[3]{3-2\sqrt{2}}\right)\)

\(=6+3\sqrt[3]{9-8}.y=6+3y\)\(\Rightarrow y^3-3y=6\left(2\right)\)

\(\left(1\right),\left(2\right)\Rightarrow P=x^3+y^3-3\left(x+y\right)+1996=x^3-3x+y^3-3y+1996\)

\(=18+6+1996=2020\)

\(P=\dfrac{2\sqrt{x}+1+\left(1-\sqrt{x}\right)\left(1+\sqrt{x}\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}:\dfrac{\sqrt{x}+2}{\sqrt{x}}\)

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

a: 13/35=1/5+1/7+1/35

b: 17/63=1/9+1/7+1/63

a: 13/35=1/5+1/7+1/35

b: 17/63=1/9+1/7+1/63

a: 1-1/2=1/2

b: 1-3/10=7/10

c:3-1/3=8/3

d: 4-1/9=35/9

e: 8-2/3=22/3

f: 5-2/5=23/5

a: bằng 1 phần 2

b: bằng 7 phần 10

c: bằng 2 phần 3

d:bằng 35 phần 9

e: bằng 22 phần 3

g: bằng 23 phần 5

chúc bn học tốt

Tổng hai phân số ban đầu là

7/9+1/5=35/45+9/45=44/45

7/9+1/5=35/45+9/45=44/45

a: \(\dfrac{5}{3}\cdot\dfrac{4}{5}=\dfrac{4}{3}\)

b: \(\dfrac{2}{3}\cdot\dfrac{3}{5}=\dfrac{2}{5}\)

c: \(\dfrac{7}{6}\cdot\dfrac{6}{5}=\dfrac{7}{5}\)

d: \(\dfrac{8}{5}\cdot\dfrac{5}{7}=\dfrac{8}{7}\)

e: \(\dfrac{7}{6}\cdot\dfrac{6}{7}=\dfrac{7}{7}=1\)

g: \(\dfrac{9}{5}\cdot\dfrac{5}{2}=\dfrac{9}{2}\)

h: \(\dfrac{4}{3}\cdot\dfrac{3}{5}=\dfrac{4}{5}\)

\(a,\dfrac{13}{4}\times\dfrac{2}{3}\times\dfrac{4}{13}\times\dfrac{3}{2}=\left(\dfrac{13}{4}\times\dfrac{4}{3}\right)\times\left(\dfrac{2}{3}\times\dfrac{3}{2}\right)=1\times1=1\)

\(b,\dfrac{75}{100}+\dfrac{18}{21}+\dfrac{19}{32}+\dfrac{1}{4}+\dfrac{3}{21}+\dfrac{13}{32}=\left(\dfrac{3}{4}+\dfrac{1}{4}\right)+\left(\dfrac{18}{21}+\dfrac{3}{21}\right)+\left(\dfrac{19}{32}+\dfrac{13}{32}\right)=1+1+1=3\\ c,\dfrac{4}{7}\times\dfrac{5}{6}+\dfrac{4}{7}\times\dfrac{1}{6}=\dfrac{4}{7}\times\left(\dfrac{5}{6}+\dfrac{1}{6}\right)=\dfrac{4}{7}\times1=\dfrac{4}{7}\\ d,\dfrac{3}{5}\times\dfrac{7}{9}-\dfrac{3}{5}\times\dfrac{2}{9}=\dfrac{3}{5}\times\left(\dfrac{7}{9}-\dfrac{2}{9}\right)=\dfrac{3}{5}\times\dfrac{5}{9}=\dfrac{1}{3}\)

\(e,\dfrac{5}{9}\times\dfrac{1}{4}+\dfrac{4}{9}\times\dfrac{3}{12}=\dfrac{5}{9}\times\dfrac{1}{4}+\dfrac{4}{9}\times\dfrac{1}{4}=\dfrac{1}{4}\times\left(\dfrac{5}{9}+\dfrac{4}{9}\right)=\dfrac{1}{4}\times1=\dfrac{1}{4}\\ f,\dfrac{7}{9}\times\dfrac{8}{5}\times\dfrac{3}{5}=\dfrac{56}{75}\\ g,\dfrac{2}{5}\times\dfrac{3}{4}+\dfrac{3}{4}\times\dfrac{3}{5}=\dfrac{3}{4}\times\left(\dfrac{2}{5}+\dfrac{3}{5}\right)=\dfrac{3}{4}\times1=\dfrac{3}{4}\\ h,\dfrac{2006}{2005}\times\dfrac{3}{4}-\dfrac{3}{4}\times\dfrac{1}{2005}=\dfrac{3}{4}\times\left(\dfrac{2006}{2005}-\dfrac{1}{2005}\right)=\dfrac{3}{4}\times1=\dfrac{3}{4}\)

a: \(=\dfrac{13}{4}\cdot\dfrac{4}{13}\cdot\dfrac{2}{3}\cdot\dfrac{3}{2}=1\cdot1=1\)

b: \(=\dfrac{3}{4}+\dfrac{1}{4}+\dfrac{6}{7}+\dfrac{1}{7}+\dfrac{19}{32}+\dfrac{13}{32}=1+1+1=3\)

c: \(=\dfrac{4}{7}\left(\dfrac{5}{6}+\dfrac{1}{6}\right)=\dfrac{4}{7}\)

d: \(=\dfrac{3}{5}\left(\dfrac{7}{9}-\dfrac{2}{9}\right)=\dfrac{3}{5}\cdot\dfrac{5}{9}=\dfrac{1}{3}\)

e: \(=\dfrac{1}{4}\left(\dfrac{5}{9}+\dfrac{4}{9}\right)=\dfrac{1}{4}\)

a: =1/3x7/5=7/15

b: =11/9x1/2=11/18

c: =1/3x3/4=1/4

d: =1/5x4/5=4/25

e: =2/3x1/4=2/12=1/6

f: =1/2x1/3=1/6

g: =1/3x1/2=1/6