\(\frac{\left(43-11\right)\left(43+11\right)}{\left(36,5-27,5\right)\left(36,5+27,5\right)}=\frac{32.54}{9.64}\)

\(=3\)

dùng hằng đẳng thức thứ 3 ta có

(43-11)(43+11) và (36,5-27,5)(36,5+27,5)

Nên =1728 : 576=3

\(R=\frac{43^2-11^2}{36,5^2-27,5^2}\)

\(R=\frac{\left(43-11\right)\left(43+11\right)}{\left(36,5+27,5\right)\left(36,5-27,5\right)}\)

\(R=\frac{32.54}{64.9}\)

\(R=3\)

\(R=\frac{43^2-11^2}{\left(36,5\right)^2-\left(27,5\right)^2}\)

    \(=\frac{\left(43-11\right)\left(43+11\right)}{\left(36,5-27,5\right)\left(36,5+27,5\right)}\)

    \(=\frac{32.54}{9.64}\)

    \(=\frac{6}{2}=3\)

Bạn viết sai đề bài rồi

\(S=\frac{97^3+83^3}{180}-97.83\)

  \(=\frac{\left(97+83\right)\left(97^2-97.83+83^2\right)}{180}-97.83\)

   \(=97^2-97.83+83-97.83\)

    \(=\left(97-83\right)^2=14^2=196\)

Trả lời:

\(R=\frac{43^2-11^2}{36,5^2-27,5^2}\)

\(R=\frac{\left(43-11\right).\left(43+11\right)}{\left(36,5-27,5\right).\left(36,5+27,5\right)}\)

\(R=\frac{32.54}{9.64}\)

\(R=3\)

Đề bài sai bạn nhé 

\(S=\frac{97^3+83^3}{180}-97.83\)

\(S=\frac{\left(97+83\right).\left(97^2-97.23+83^2\right)}{180}-97.83\)

\(S=97^2-97.83+83^2-97.83\)

\(S=97^2-2.97.83+83^2\)

\(S=\left(97-83\right)^2\)

\(S=14^2\)

\(S=196\)

11) \(\dfrac{5}{7}\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{4}{7}\right)+\left(\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{4}{7}\right):\dfrac{7}{5}\)

= \(\dfrac{5}{7}\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{4}{7}\right)+\left(\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{4}{7}\right)\cdot\dfrac{5}{7}\)

= \(\dfrac{5}{7}\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{4}{7}+\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{4}{7}\right)\)

= \(\dfrac{5}{7}\cdot0\)

=0

12) \(\dfrac{43}{5}\left(\dfrac{17}{3}-\dfrac{16}{9}+2\right)-\dfrac{43}{5}\left(\dfrac{17}{3}-\dfrac{16}{9}\right)\)

= \(\dfrac{43}{5}\left(\dfrac{17}{3}-\dfrac{16}{9}+2-\dfrac{17}{3}+\dfrac{16}{9}\right)\)

= \(\dfrac{43}{5}\cdot2=\dfrac{43}{10}\)

11, 5/7( 1/2-1/3+1/4)+ (1/3-1/2-1/4):7/5

= 5/7.(1/2 - 1/3 + 1/4 )+( 1/3 - 1/2 - 1/4). 5/7

= 5/7.(1/2 - 2/3 + 1/4 + 1/3 - 1/2 - 1/4)

= 5/7 . -1/3

= -5/21

12, 43/5.(17/3 - 16/9 + 2)- 43/5. (17/3 - 16/9)

= 43/5.( 17/3 - 16/9 + 2 - 17/3 + 16/9)

= 43/5 . 2

= 86/5

\(A=\dfrac{\left(43-11\right)\left(43+11\right)}{\left(36.5-27.5\right)\left(36.5+27.5\right)}\)

\(=\dfrac{32\cdot54}{9\cdot64}=\dfrac{1}{2}\cdot6=3\)

a) Ta có: \(\left(\dfrac{-1}{2}\right)^2\cdot\dfrac{7}{4}:\left(\dfrac{5}{8}-1\dfrac{3}{16}\right)\)

\(=\dfrac{1}{4}\cdot\dfrac{7}{4}:\left(\dfrac{5}{8}-\dfrac{19}{16}\right)\)

\(=\dfrac{1}{4}\cdot\dfrac{7}{4}:\dfrac{-9}{16}\)

\(=\dfrac{1}{4}\cdot\dfrac{7}{4}\cdot\dfrac{-16}{9}\)

\(=\dfrac{-112}{144}=\dfrac{-7}{9}\)

b) Ta có: \(17\dfrac{6}{11}\cdot\dfrac{4}{27}-8\dfrac{6}{11}:\dfrac{27}{4}+350\%\)

\(=17\dfrac{6}{11}\cdot\dfrac{4}{27}-8\dfrac{6}{11}\cdot\dfrac{4}{27}+350\%\)

\(=\dfrac{4}{27}\left(17+\dfrac{6}{11}-8-\dfrac{6}{11}\right)+\dfrac{7}{2}\)

\(=\dfrac{4}{27}\cdot9+\dfrac{7}{2}\)

\(=\dfrac{4}{3}+\dfrac{7}{2}=\dfrac{8}{6}+\dfrac{21}{6}=\dfrac{29}{6}\)