Question

[Bảo Bối Thần Kỳ]

a, \(\left(10^2+11^2+12^2\right)\div\left(13^2+14^2\right)\\ \)

b,\(1.2.3.....9-1.2.3....8-1.2.3.....7.8^2\)

c, \(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)

d, \(1152-\left(374+1152\right)+\left(-65+374\right)\)

Answer 1

[Tạ Đức Hoàng Anh]

a) Đặt \(A=\left(10^2+11^2+12^2\right)\div\left(13^2+14^2\right)\)

- Ta có: \(A=\left(100+121+144\right)\div\left(169+196\right)\)

      \(\Leftrightarrow A=365\div365=1\)

Vậy \(A=1\)

b) Đặt \(B=1.2.3.....9-1.2.3.....8-1.2.3.....8^2\)

- Ta có: \(B=1.2.3.....8.\left(9-1\right)-1.2.3.....8^2\)

     \(\Leftrightarrow B=1.2.3.....8.8-1.2.3.....8.8=0\)

Vậy \(B=0\)

c) Đặt \(C=\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)

- Ta có: \(C=\frac{3^2.4^2.2^{32}}{11.2^{13}.2^{22}-2^{36}}\)

      \(\Leftrightarrow C=\frac{3^2.2^4.2^{32}}{11.2^{35}-2^{36}}\)

      \(\Leftrightarrow C=\frac{3^2.2^{36}}{2^{35}.\left(11-2\right)}\)

      \(\Leftrightarrow C=\frac{9.2^{36}}{2^{35}.9}\)

      \(\Leftrightarrow C=2\)

Vậy \(C=2\)

d) Đặt \(D=1152-\left(374+1152\right)+\left(-65+374\right)\)

- Ta có: \(D=1152-374-1152-65+374\)

      \(\Leftrightarrow D=\left(1152-1152\right)+\left(374-374\right)-65\)

      \(\Leftrightarrow D=-65\)

Vậy \(D=-65\)