Find 3 terms of Gp whose sum and product is 19 and 216
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Let three term are a, ar, a/r
ATQ a×ar×a/r = 216
a^3=216
a=6
a+ar+a/r =19
6+6r+6/r=19
6r+6/r =13
6r^2+6=13r
6r^2-13r+6=0
r= [-(-13) +/-√13 (13)-4 (6) (6)] /2 (6)
[13+/-5] /12
If positive r= [13+5] /12 =3/2
If negative r= [13-5] /12 =2/3
So term are a, ar, a/r = 6, 9, 4 or 6, 4, 9
ATQ a×ar×a/r = 216
a^3=216
a=6
a+ar+a/r =19
6+6r+6/r=19
6r+6/r =13
6r^2+6=13r
6r^2-13r+6=0
r= [-(-13) +/-√13 (13)-4 (6) (6)] /2 (6)
[13+/-5] /12
If positive r= [13+5] /12 =3/2
If negative r= [13-5] /12 =2/3
So term are a, ar, a/r = 6, 9, 4 or 6, 4, 9
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