Question

Bai 12 tính nhanh

A = 123 ( 123 + 154 ) + 77²

B = 3²⁴ -(27⁴+1)(9⁶-1)

C=85²+75²+65²+55²-45²-35²-25²-15²

Answer 1

a) \(A=123\left(123+154\right)+77^2\)

\(A=123^2+\left(123.154\right)+77^2=\left(123+77\right)^2=200^2=400\)

b) \(B=3^{24}-\left(2^{47}+1\right)\left(9^6-1\right)\)

\(B=3^{24}-\left(3^{12}-1\right)\left(3^{12}+1\right)\)

\(B=3^{24}-3^{24}+1=1\)

c) \(C=85^2+75^2+65^2+55^2-45^2-35^2-25^2-15^2\)

\(C=\left(85^2-15^2\right)+\left(75^2-25^2\right)+\left(65^2-35^2\right)+\left(55^2-45^2\right)\)

\(C=\left(85+15\right)\left(85-15\right)+\left(75+25\right)\left(75-25\right)+\left(65+35\right)\left(65-35\right)\left(55+45\right)\left(55-45\right)\)

\(C=100\left(60+50+40+30+20+10\right)\)

\(C=100.210=21000\)

Answer 2

A=40000

B=1

C=16000