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