Question

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Answer 1

Explicación paso a paso:

5.

a - b = b - c

a + c = 2b

(a+c)² = 4b²

b² - ac = 25

4b² - 4ac = 100

(a+c)² - 4ac = 100

a² + 2ac + c² - 4ac = 100

a² - 2ac + c² = 100

(a-c)² = 100

a-c = 10

Nos piden la diferencia de los términos extremos

a - c = 10

6.

a/b = c/d = k

ad = bc

a = bk

c = dk

a+c = 35

b-d = 2

(a+c)(b-d) = 70

ab - ad + cb - cd = 70

ab - cb + cb - cd = 70

ab - cd = 70

b²k - d²k = 70

k(b² - d²) = 70

k(b-d)(b+d) = 2×5×7

b-d= 5

b+d = 7

b = 6

d = 1

máximo valor de los consecutivos: 6

7.

a/b = c/d = 3/4

a = (3/4)b

c = (3/4)d

a/c = (5/4)

a = 5k, c = 4k

b = 20k/3 , d = 44k/3

b × d = 880

20k/3 × 44k/3 = 880

880k²/9 = 880

K² = 9

k = 3

Piden hallar la cuarta proporcional

d = 44k/3 = 44×3/3 = 44