Question

Determinati numerele nenule x y z stiind ca 1/x=2/y=3/z=4/t si x+y/2+z/3+t/4=1/8

Answer 1

1/x = 2/y = 3/z = 4/t = k

x = 1/k, y = 2/k, z = 3/k, t = 4/k

x + y/2 + z/3 + t/4 = 1/8

1/k + 1/k + 1/k + 1/k = 1/8

4/k = 1/8

k = 4 * 8/1 = 32

Atunci x = 1/k = 1/32

y = 2/k = 2/32 = 1/16

z = 3/k = 3/32

t = 4/k = 4/32 = 1/8