Three numbers x, y, and z are in the ratio 2: 7: 8. if 12 is subtracted from y, then three numbers form a geometric sequence (in the order x, y–12, z). find x, y, and z. there are 2 sets.

  (X, Y, Z) = (8, 28, 32)

Step-by-step explanation:

The ratio units will form a geometric sequence if the middle one is the square root of the first and last:

  Y' = √(2·8) = 4

To get this value from 7, we must subtract 3. In the real sequence we must subtract 12, so each "ratio unit" must stand for 12/3 = 4 real units, and the real numbers X, Y, Z are 2·4 = 8, 7·4 = 28, 8·4 = 32.

  (X, Y, Z) = (8, 28, 32)

  (X, Y-12, Z) = (8, 16, 32) . . . . a geometric sequence with a ratio of 2

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step-by-step explanation: easy math