Bài 1: Biết `1^2 + 2^2 + 3^2 +…+12^2 = 650` Tính `a) A = 2^2 + 4^2 + 6^2 +…+24^2` `b) B = 1^2 + 3^2 + 6^2 + 9^2 +….+36^

2 bình luận về “Bài 1: Biết `1^2 + 2^2 + 3^2 +…+12^2 = 650` Tính `a) A = 2^2 + 4^2 + 6^2 +…+24^2` `b) B = 1^2 + 3^2 + 6^2 + 9^2 +….+36^”

1. Bài 1:

   a) A = 2^2 + 4^2 +6^2+…+24^2

   A = (2.1)^2 + (2.2)^2 + (2.3)^2 +…+(2.12)^2

   A = 2^2 . 1^2 + 2^2 . 2^2 + 2^2 . 2^3 + …+ 2^2 . 2^12

   A = 2^2 . ( 1^2 + 2^2 +3^2 + ….+12^2)

   A = 2^2 . 650

   A = 4 . 650

   A = 2600

   b) B = 1^2 + 3^2 + 6^2 + 9^2 +…+ 36^2

   B = 1^2 +(3^2 + 6^2 + 9^2 +…+ 36^2)

   B = 1^2 +[(3.1)^2 + (3.2)^2 + (3.3)^2 +….+ (3.12)^2]

   B = 1^2 + 3^2 .( 1^2 + 2^2 +3^2 + ….+12^2)

   B = 1 + 9 . 650

   B = 1 + 5850

   B = 5851

   Bài 2:

   3/5 . 2^x + 7/5 . 2^(x+3) = 3/5 . 2^10 + 7/5 . 2^13

   3/5 . 2^x + 7/5 . 2^x . 2^3 = 3/5 . 2^10 + 7/5 .2^10 . 2^3

   2^x . (3/5+7/5. 2^3)=2^10.(3/5+7/5. 2^3)

   2^x = 2^10

   x = 10

   Vậy x = 10

   Trả lời
2. Bài 1:

   a) A = 2^2 + 4^2 +6^2+…+24^2

   A = (2.1)^2 + (2.2)^2 + (2.3)^2 +…+(2.12)^2

   A = 2^2 . 1^2 + 2^2 . 2^2 + 2^2 . 2^3 + …+ 2^2 . 2^12

   A = 2^2 . ( 1^2 + 2^2 +3^2 + ….+12^2)

   A = 2^2 . 650

   A = 4 . 650

   A = 2600

   b) B = 1^2 + 3^2 + 6^2 + 9^2 +…+ 36^2

   B = 1^2 +(3^2 + 6^2 + 9^2 +…+ 36^2)

   B = 1^2 +[(3.1)^2 + (3.2)^2 + (3.3)^2 +….+ (3.12)^2]

   B = 1^2 + 3^2 .( 1^2 + 2^2 +3^2 + ….+12^2)

   B = 1 + 9 . 650

   B = 1 + 5850

   B = 5851

   Bài 2:

   3/5 . 2^x + 7/5 . 2^(x+3) = 3/5 . 2^10 + 7/5 . 2^13

   3/5 . 2^x + 7/5 . 2^x . 2^3 = 3/5 . 2^10 + 7/5 .2^10 . 2^3

   2^x . (3/5+7/5. 2^3)=2^10.(3/5+7/5. 2^3)

   2^x = 2^10

   x = 10

   Vậy x = 10

   Trả lời