Question

[duong thuy Tram]

tính nhanh

a)A=5⁴.3⁴-(15²-1)(15²+1)

b)C=50²-49²+48²-47²+...+2²-1²

Answer 1

[Mysterious Person]

a) \(A=5^4.3^4-\left(15^2-1\right)\left(15^2+1\right)=\left(5.3\right)^4-\left(\left(15^2\right)^2-1^2\right)\)

\(=15^4-\left(15^4-1\right)=15^4-15^4+1=1\)

b) \(C=50^2-49^2+48^2-47^2+...+2^2-1^2\)

\(=\left(50^2-49^2\right)+\left(48^2-47^2\right)+...+\left(2^2-1^2\right)\)

\(=\left(50-49\right)\left(50+49\right)+\left(48-47\right)\left(48+47\right)+...+\left(2-1\right)\left(2+1\right)\)

\(=1.99+1.95+...+1.3=99+95+...+3\)

\(=\left(99+3\right)+\left(95+7\right)+...+\left(55+47\right)+51\)

\(=102+102+...+102+51\)

số lượng con số \(102\) là \(\dfrac{25-1}{2}=12\)

\(\Rightarrow C=102.12+51=1224+51=1275\)