\(x=\sqrt[3]{9+4\sqrt{5}}+\sqrt[3]{9-4\sqrt{5}}\\ \Leftrightarrow x^3=9+4\sqrt{5}+9-4\sqrt{5}+3\sqrt[3]{\left(9-4\sqrt{5}\right)\left(9+4\sqrt{5}\right)}\left(\sqrt[3]{9+4\sqrt{5}}+\sqrt[3]{9-4\sqrt{5}}\right)\\ \Leftrightarrow x^3=18+3x\sqrt[3]{81-80}=18-3x\\ \Leftrightarrow x^3-3x=18\\ y=\sqrt[3]{3-2\sqrt{2}}+\sqrt[3]{3+2\sqrt{2}}\\ \Leftrightarrow y^3=6+3\sqrt[3]{\left(3-2\sqrt{2}\right)\left(3+2\sqrt{2}\right)}\left(\sqrt[3]{3-2\sqrt{2}}+\sqrt[3]{3+2\sqrt{2}}\right)\\ \Leftrightarrow y^3=6+3y\sqrt[3]{9-8}=6+3y\\ \Leftrightarrow y^3-3y=6\\ \Leftrightarrow P=x^3+y^3-3\left(x+y\right)+1993\\ P=x^3+y^3-3x-3y+1993=18+6+1993=2017\)

Áp dụng: \(\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3=a^3+b^3+3ab\left(a+b\right)\)

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

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

\(=18+3\sqrt[3]{81-80}.x=18+3x\)

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

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

\(=6+3\sqrt[3]{9-8}y=6+3y\)

\(P=x^3+y^3-3\left(x+y\right)+1993\)

\(=18+3x+6+3y-3x-3y+1993=2017\)

a) \(\left(\dfrac{1}{6}+\dfrac{5}{9}\right)+\dfrac{4}{9}\)

\(=\dfrac{1}{6}+\dfrac{5}{9}+\dfrac{4}{9}\)

\(=\dfrac{1}{6}+1\)

\(=\dfrac{7}{6}\)

b) \(\dfrac{3}{17}+\left(\dfrac{14}{17}-\dfrac{2}{3}\right)\)

\(=\dfrac{3}{17}+\dfrac{14}{17}-\dfrac{2}{3}\)

\(=1-\dfrac{2}{3}\)

\(=\dfrac{1}{3}\)

c) \(\left(\dfrac{3}{2}-\dfrac{2}{3}\right)+\dfrac{7}{6}\)

\(=\left(\dfrac{9}{6}-\dfrac{4}{6}\right)+\dfrac{7}{6}\)

\(=\dfrac{13}{6}+\dfrac{7}{6}\)

\(=\dfrac{20}{6}\)

`a, 3/4 + 1/2 xx 7/2`

`= 3/4 + 7/4`

`=10/4`

`=5/2`

`b, 6/15 - 1/3 : 5/3`

`= 6/15 - 1/3 xx 3/5`

`= 6/15 - 3/15`

`= 3/15`

`=1/5`

`c, x-4/9 = 3/7 : 9/4`

`=> x-4/9= 3/7 xx 4/9`

`=> x-4/9= 12/63`

`=> x-4/9=4/21`

`=> x= 4/21 +4/9`

`=>x= 40/63`

`d, 7/9 xx 3/5 -1/2=1/5`

`->` sao lại bằng có `x` ko vậy ạ?

`a,`

`3/4+1/2 \times 7/2=3/4+7/4=10/4=5/2`

`b,`

`6/15 - 1/3 \div 5/3=6/15-1/5=1/5`

`c,` Tìm x?

`x-4/9=3/7 \div 9/4`

`x-4/9=4/21`

`x=4/21+4/9`

`x=40/63`

`d, 7/9x \times 3/5-1/2=1/5`

`7/9x \times 3/5=1/5+1/2`

`7/9x \times 3/5=7/10`

`7/9x=7/10 \div 3/5`

`7/9x=7/6`

`x=7/6 \div 7/9=3/2`

\(7\frac{5}{9}-\left(3\frac{5}{9}-2\frac{3}{4}\right)=7\frac{5}{9}-3\frac{5}{9}+2\frac{3}{4}=4+2\frac{3}{4}=6\frac{3}{4}\)

a.7 5/9-(3 5/9-2 3/4)

=7 5/9-3 5/9+2 3/4

=4+2 3/4

=6 3/4

#)Giải :

\(7\frac{5}{9}-\left(3\frac{5}{9}-2\frac{3}{4}\right)\)

= \(7\frac{5}{9}-\left(-3\frac{5}{9}\right)+2\frac{3}{4}\)

= \(7\frac{5}{9}+3\frac{5}{9}+2\frac{3}{4}\)

= \(10\frac{5}{9}+2\frac{3}{4}\)

= \(13\frac{11}{36}\)

            #~Will~be~Pens~#

\(7\frac{5}{9}-\left(3\frac{5}{9}-2\frac{3}{4}\right)=7\frac{5}{9}-3\frac{5}{9}+2\frac{3}{4}=4+2\frac{3}{4}=6\frac{3}{4}\)

\(4^3:8\cdot3^2-5^2+9\)

\(=8\cdot9-25+9\)

=81-25

=56