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8 tháng 8 2020

A = 1002 - 992 + 982 - 972 + ...... + 22 - 12

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

= 1 + 2 + 3 + ......... + 99 + 100

= ( 100 + 1 ) . 100 : 2 = 5050 

 B = 3 ( 22 + 1 ) ( 24 + 1 ) ... ( 264 + 1 ) + 12

= ( 22 - 1 ) ( 22 + 1 ) ( 24 + 1 ) ... ( 264 + 1 ) + 1

= ( 24 - 1 ) ( 24 + 1 ) ... ( 264 + 1 ) + 1

= ( 28 - 1 ) ( 28 + 1 ) ... ( 264 + 1 ) + 1

= ( 216 - 1 ) ( 216 + 1 ) ... ( 264 + 1 ) + 1

= ( 232 - 1 ) ( 232 + 1 ) ( 264 + 1 ) + 1

= ( 264 - 1 ) ( 264 + 1 ) + 1

= 2128 - 1 + 1 

= 2128

C = ( a + b + c )2 + ( a + b - c )2 - 2 ( a + b )2

= a2 + b2 + c2 + 2ab + 2bc + 2ca + a2 + ab - ac + ab + b2 - bc - ac - bc + c2 - 2 ( a2 + 2ab + b2 )

= a2 + b2 + c2 + 2ab + 2bc + 2ca + a2 + ab - ac + ab + b2 - bc - ac - bc + c2 - 2a2 - 4ab - 2b2

= 2c2

8 tháng 8 2020

Bài làm:

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

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

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

\(A=\frac{\left(100+1\right)\times100}{2}=5050\)

b) \(B=3\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1^2\)

\(B=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)

\(B=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)

...

\(B=\left(2^{64}-1\right)\left(2^{64}+1\right)+1\)

\(B=2^{128}-1+1=2^{128}\)

c) \(C=\left(a+b+c\right)^2+\left(a+b-c\right)^2-2\left(a+b\right)^2\)

\(C=a^2+b^2+c^2+2\left(ab+bc+ca\right)+a^2+b^2+c^2+2\left(ab-bc-ca\right)-2a^2-4ab-2b^2\)

\(=2c^2+2\left(ab+bc+ca+ab-bc-ca-2ab\right)\)

\(=2c^2+2.0=2c^2\)

18 tháng 9 2021

\(A=\left(100-99\right)\left(100+99\right)+\left(99-98\right)\left(98+97\right)+...+\left(2-1\right)\left(2+1\right)\\ A=100+99+99+98+...+2+1\\ A=\left(100+1\right)\left(100-1+1\right):2=5050\)

\(B=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\\ B=\left(2^1-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)...\left(2^{64}+1\right)+1\\ B=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)...\left(2^{64}+1\right)+1\\ B=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)...\left(2^{64}+1\right)+1\\ B=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)+1\\ B=\left(2^{32}-1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)+1\\ B=\left(2^{64}-1\right)\left(2^{64}+1\right)+1=2^{128}-1+1=2^{128}\)

\(C=a^2+b^2+c^2+2ab+2bc+2ac+a^2+b^2+c^2+2ab-2ac-2bc-2a^2-4ab-2b^2\\ C=2c^2\)

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

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

=5050

b: \(B=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\cdot...\cdot\left(2^{64}+1\right)+1\)

\(=\left(2^4-1\right)\left(2^4+1\right)\cdot...\cdot\left(2^{64}+1\right)+1\)

\(=\left(2^8-1\right)\left(2^8+1\right)\cdot...\cdot\left(2^{64}+1\right)+1\)

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)+1\)

\(=\left(2^{32}-1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)+1\)

\(=\left(2^{64}-1\right)\cdot\left(2^{64}+1\right)+1\)

\(=2^{128}-1+1=2^{128}\)

20 tháng 2 2022

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

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

\(=199+195+...+3\)

\(=\dfrac{\left(199+3\right)\left(\dfrac{199-3}{4}+1\right)}{2}=5050\)

b. \(B=3\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1^2\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1^2\)

\(=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1^2\)

\(=2^{128}-1+1=2^{128}\)

c) \(C=\left(a+b+c\right)^2+\left(a+b-c\right)^2-2\left(a+b\right)^2\)

\(=a^2+b^2+c^2+2ab+2ac+2bc+a^2+b^2+c^2+2ab-2ac-2bc-2a^2-2b^2-4ab\)

\(=2c^2\)

13 tháng 10 2021

\(2,\\ a,a^3+b^3=a^3=3a^2b+3ab^2+b^3-3a^2b-3ab^2\\ =\left(a+b\right)^3-3ab\left(a+b\right)\\ b,a^3+b^3+c^3-3abc\\ =\left(a+b\right)^3-3ab\left(a+b\right)+c^3-3abc\\ =\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2\right)-3ab\left(a+b+c\right)\\ =\left(a+b+c\right)\left(a^2+b^2+c^2-ac-ab-bc\right)\)

13 tháng 10 2021

khó v. e ko giải đc đâu

 

20 tháng 10 2021

các bn giúp mình nhé

20 tháng 10 2021

chụp khó nhìn quá bn ơi

a: A=(100-99)(100+99)+(98-97)(98+97)+...+(2-1)(2+1)

=100+99+98+...+2+1

=5050

b: \(B=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\cdot...\cdot\left(2^{64}+1\right)+1\)

\(=\left(2^4-1\right)\left(2^4+1\right)\cdot...\cdot\left(2^{64}+1\right)+1\)

\(=\left(2^8-1\right)\left(2^8+1\right)\cdot...\cdot\left(2^{64}+1\right)\)+1

\(=2^{64}-1+1=2^{64}\)