Question

Aflati nr rationale a,b,c stiind ca 0,(3)a=0,25b=0,2c si 3ab+5bc-4ac=304

Answer 1

Răspuns:

Explicație pas cu pas:

0,(3) = 3/9 = 1/3

0,25 = 25/100 = 1/4

0,2 = 2/10 = 1/5

a/3 = b/4 = c/5 = k

a = 3k

b = 4k

c = 5k

3*3k*4k + 5*4k*5k - 4*3k*5k = 304

36k^2 + 100k^2 - 60k^2 = 304

76k^2 = 304

k^2 = 304/76 = 4

k = 2 sau -2

k = 2

a = 6; b = 8; c = 10

k = -2

a = -6; b = -8; c = -10