Question

The product of three consecutive terms of a G.P is 216 and the sum of their squares is

133.Find the terms.​

Answer 1

Answer:

Let the three terms be a/r, a and ar.

According to the first condition.

» a³ = 216 = 6

According to the second condition.

» a² (1/r² + 1 + r²) = 133

» (1 + r⁴)/r² = 133/36 - 1

» (1 + r⁴)/r² = 97/36

» 36r⁴ - 97r² + 36 = 0

» r² = [97 ± √4225]/72

» r² = (97 ± 65)/72

» r² = 162/72 or 32/72

» r² = 81/36 or 16/36

» r = ±9/6 or ±4/6

» r = ±3/2 or ±2/3

Case 1. r = 3/2

» a/r = 6 / (3/2) = 4

» a = 6

» ar = 6 (3/2) = 9

Case 2. r = - 3/2

» a/r = 6 / (-3/2) = - 4

» a = 6

» ar = 6 (-3/2) = - 9

Case 3. r = 2/3

» a/r = 6 / (2/3) = 9

» a = 6

» ar = 6 (2/3) = 4

Case 4. r = -2/3

» a/r = 6 / (-2/3) = -9

» a = 6

» ar = 6 (-2/3) = -4