giai giup voi

\(10^2=100\)

\(10^3=1000\)

\(10^4=10000\)

\(10^5=100000\)

\(10^6=1000000\)

\(10^2=100;10^3=1000;10^4=10000;10^5=100000;10^6=1000000\)

a) (a + b)² = a² + 2ab + b²

a) (a + b)² = a² + 2ab + b²

               = a² - 2ab + b² + 4ab

               = (a - b)² + 4ab

         Thay a - b = 8 và ab = 10, ta có : 

    (a - b)² + 4ab = 8² + 4*10 = 64 + 40 = 104

Vậy (a + b)² = 104

b) a³ - b³ = (a - b)(a² + ab + b²) (1) 

Ta có : 

    a - b = 8

=> (a - b)² = 8²

   a² - 2ab + b² = 64

     a² + b² = 64 - 2ab

            mà ab = 4 nên

      a² + b² = 64 - 2*4 = 64 - 8 = 56 ⁽²⁾

Thay (2) vào (1), ta có 

(a - b)(a² + ab + b²) = (a - b)(56 + ab)

      mà a - b = 8 và ab = 4 nên

(a - b)(56 + ab) = 8*(56 + 4) = 8*60 = 480

Vậy a³ - b³ = 480;

\(A=\frac{2^{10}.13+2^{10}.65}{2^8.104}=\frac{2^{10}.\left(13+65\right)}{2^8.2^3.13}=\frac{2^{10}.78}{2^{11}.13}=\frac{78}{2.13}=\frac{78}{26}=3\)

\(\frac{3}{10}.\left(-\frac{5}{9}+\frac{3}{5}\right)-\frac{3}{10}.\left(\frac{3}{9}+\frac{-2}{5}\right)\)

=\(\frac{3}{10}.\frac{2}{45}-\frac{3}{10}.\left(-\frac{1}{15}\right)\)

\(=\frac{3}{10}.\left(\frac{2}{45}-\left(-\frac{1}{15}\right)\right)\)

\(=\frac{3}{10}.\frac{1}{9}=\frac{1}{30}\)

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