\(B=\frac{780^2-220^2}{125^2+150.125+75^2}\)\(=\frac{\left(780+220\right).\left(780-220\right)}{\left(125+75\right)^2}\)\(=\frac{1000.560}{200^2}\)\(=\frac{560000}{40000}=14\)

a:

Số số hạng trong dãy M là:

(1002-12):10+1=100(số)

=>Sẽ có 50 cặp (1002;992); (982;972);....;(22;12) có hiệu bằng 10

\(M=1002-992+982-972+...+22-12\)

\(=\left(1002-992\right)+\left(982-972\right)+...+\left(22-12\right)\)

\(=10+10+...+10\)

=10*50=500

b: \(N=\left(202+182+...+42+22\right)-\left(192+172+...+32+12\right)\)

\(=\left(202-192\right)+\left(182-172\right)+...+\left(22-12\right)\)

=10+10+...+10

=10*10=100

\(A=\left(100^2-99^2\right)+\left(98^2-97^2\right)+...+\left(2^2-1^2\right)\)

\(=\left(100-99\right)\left(100+99\right)+\left(98-97\right)\left(98+97\right)+...+\left(2-1\right)\left(2+1\right)\)

\(=100+99+98+97+...+2+1\)

\(=\left(100+1\right).\frac{100-1}{2}=\frac{101.99}{2}=\frac{9999}{2}\)

\(\left(780^2-220^2\right):\left(125^2+150\cdot125+75^2\right)\)

\(=\dfrac{1000\cdot540}{200^2}\)

\(=\dfrac{10000\cdot54}{40000}=\dfrac{54}{4}=\dfrac{27}{2}\)

a) \(=\left(127+73\right)^2=200^2=40000\)

b) \(=18^8-\left(18^8-1\right)=1\)

c) \(=\left(100+99\right)\left(100-99\right)+\left(98+97\right)\left(98-97\right)+...+\left(2+1\right)\left(2-1\right)\)

\(=100+99+98+97+...+2+1=5050\)

d) biến đổi thành \(20^2-19^2+18^2-17^2+..+2^2-1^2\)

rồi giải ra như trên

vào câu hỏi tương tự 

lik-e cho mình nhé

Bạn hãy click vào trong câu hỏi tương tự nhé !

a) 127² + 146.127 + 73²

= 127² + 2.73.127 + 73²

= (127 + 73)² = 200² = 40000

b) 9⁸ . 2⁸ - (18⁴ - 1)(18⁴ + 1)

= (9.2)⁸ - 18⁸ + 1

= 18⁸ - 18⁸ + 1 = 1

c) \(\frac{780^2-220^2}{125^2+150.125+75^2}=\frac{\left(780-220\right)\left(780+220\right)}{125^2+2.75.125+75^2}=\frac{560.1000}{\left(125+75\right)^2}=\frac{560000}{200^2}\)

\(=\frac{560000}{40000}=14\)

a) 127² + 146.127 + 73²

= 127² + 2.73.127 + 73²

= ( 127 + 73 )²

= 200² = 40 000

b) 9⁸.2⁸ - ( 18⁴ - 1 )( 18⁴ + 1 ) 

= ( 9.2 )⁸ - [ ( 18⁴ )² - 1² ]

= 18⁸ - 18⁸ + 1

= 1

c) \(\frac{780^2-220^2}{125^2+150\cdot125+75^2}\)

\(=\frac{\left(780-220\right)\left(780+220\right)}{125^2+2\cdot75\cdot125+75^2}\)

\(=\frac{560\cdot1000}{\left(125+75\right)^2}\)

\(=\frac{560000}{200^2}\)

\(=\frac{560000}{40000}=14\)

             Bài làm :

a) 127² + 146.127 + 73²

= 127² + 2.73.127 + 73²

= ( 127 + 73 )²

= 200² 

= 40 000

b) 9⁸.2⁸ - ( 18⁴ - 1 )( 18⁴ + 1 ) 

= ( 9.2 )⁸ - [ ( 18⁴ )² - 1² ]

= 18⁸ - 18⁸ + 1

= 1

 \(\text{c)}\frac{780^2-220^2}{125^2+150\cdot125+75^2}\)

\(=\frac{\left(780-220\right)\left(780+220\right)}{125^2+2\cdot75\cdot125+75^2}\)

\(=\frac{560\cdot1000}{\left(125+75\right)^2}\)

\(=\frac{560000}{200^2}\)

\(=\frac{560000}{40000}\)

\(=14\)