Question

The sum of three terms in G.P is 26 and their product is 216. find them​

Answer 1

Step-by-step explanation:Let three terms of GP be ar,a,a∗r

Their product will be

ab∗a∗a∗r=216

a3=216=6∗6∗6

a=(63)1/3

a=6

Now sum of these numbers

ar+a+a∗r=26

a+a∗r+a∗r2r=26

a+a∗r+a∗r2=26r

Now putting value of a

6+6r+6r2=26r

6r2+6r−26r+6=0

6r2−20r+6=0

2(3r2−10r+3)=0

3r2−10r+3=0

3r2−9r−r+3=0

3r(r−3)−1(r−3)=0

(3r−1)(r−3)=0

r=13orr=3

So GP will be

a/r=18or2

a=6

a∗r=2or18

Therefore G.P will be

18,6,2or2,6,18