Question

Tính nhanh: 80²-75²+70²-65²+60²-55²+........+10²-5²

Answer 1

\(=\left(80-75\right)\left(80+75\right)+\left(70-65\right)\left(75+65\right)+...+\left(10-5\right)\left(10+5\right)\)  

\(=5\cdot155+5\cdot135+..+5\cdot15\) 

\(=5\cdot\left(155+135+...+15\right)\)  

\(=5\cdot\left(155+15+135+35+115+55+95+75\right)\) 

\(=5\cdot\left(170\cdot4\right)\)  

\(=5\cdot680=3400\) 

Answer 2

haizz

Answer 3

80² - 75² + 70² - 65² + 60² - 55² + ... + 10² - 5²

= ( 80² - 75² ) + ( 70² - 65² ) + ( 60² - 55² ) + ... + ( 10² - 5² )

= ( 80 - 75 )( 80 + 75 ) + ( 70 - 65 )( 70 + 65 ) + ... + ( 10 - 5 )( 10 + 5 )

= 5.155 + 5.135 + ... + 5.15

= 5( 155 + 135 + ... + 15 )

= \(5\left\{\frac{\left(155+15\right)\left[\left(155-15\right):20+1\right]}{2}\right\}\)

= 5.680

= 3400