Question

[Hoàng Mỹ Linh]

Tính nhanh: 

a) \(85^2+75^2+65^2+55^2-45^2-35^2-25^2-15^2\)

b) \(\frac{135^2+130.135+65^2}{135^2-65^2}\)

c) \(1^2-2^2+3^2-4^2+5^2-...+2011^2-2012^2\)

d) \(10\left(9^2+1\right)\left(9^4+1\right)\left(9^8+1\right)\left(9^{16}+1\right)\left(9^{32}+1\right)-9^{64}\)

Thanks mấy bạn nhiều ạ.....Mình sẽ tick cho tất cả mọi người  

Answer 1

[Lê Hiếu Ngân]

a) \(85^2+75^2+65^2+55^2-45^2-35^2-25^2-15^2\)

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

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

\(=70.100+50.100+30.100+10.100\)

\(=7000+5000+3000+1000\)

\(=16000\)

Answer 2

[Lê Hiếu Ngân]

b) \(\frac{135^2+130.135+65^2}{135^2-65^2}\)

\(=\frac{135^2+2.60.135+65^2}{135^2-65^2}\)

\(=\frac{\left(135+65\right)^2}{\left(135-65\right)^2}\)

\(=\frac{200^2}{70^2}\) \(=\frac{200}{70}=\frac{20}{7}\)