Question

Ex 25
Va rog
Dau coroana

Answer 1

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Answer 2

25)

x / 6 = y / 8 = z / 9 = k

⇒  x = 6 k;  y = 8 k;   z = 9 k

x · y · z = 54

6 k · 8 k · 9 k = 54

k³ = 54 / ( 6 · 8 · 9 ) =  54 / ( 54  · 8 ) = 1 / 8 = 1·³ / 2³

k = ∛( 1³ / 2³) = 1 / 2

x = 6 · 1 / 2 = 3 ;   y = 8 · 1 / 2 = 4;  z = 9 · 1 / 2 = 4,5

x = 3;   y = 4;  z = 4,5

Verific:   3 × 4 × 4,5 = 3 × 18 = 54 → produsul celor 3 numere

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b)

5 / x = 2 / y = 25 / z = k   ⇒  x = 5 / k;   y = 2 / k  si z = 25 / k

5 / k  ×  2 / k  ×  25 / k = 54  

( 5 × 2 × 25 ) / k³ = 54

54 k³ = 250

k³ = 250 / 54 = 125 / 27 = 5³ / 3³ = ( 5 / 3 )³

k = ∛( 5 / 3 )³

k = 5 / 3

x =  5  : 5 / 3 = 5 ·  3 / 5 = 3

y = 2 : 5 / 3 = 2 · 3 / 5 = 6 / 5

z = 25 : 5 / 3 = 25 · 3 / 5 = 15

x = 3;  y = 6 / 5   si z = 15

Verific : 3 × 6 / 5 × 15 = 54 → produsul celor 3 numere