Question

Sum of 3 no.of G.P is 39,their product is 729.find the number

Answer 1

a=9 and r=(3/9) or 3.....

Answer 2

Answer:

The three numbers are 3, 9, 27    

Step-by-step explanation:

Given that sum of 3 numbers of G.P is 39 and their product is 729.

we have to find the number.

$\text{Let the three numbers are }\frac{a}{r}, a, ar$

As the product of three numbers is 729

$\frac{a}{r}\times a\times ar=729$

$a^3=729$

Taking cube root on both sides, we get

$a=9$

As sum of three numbers is 39

$\frac{a}{r}+a+ar=39$

$\frac{9}{r}+9+9r=39$

$\frac{9}{r}+9r=30$

$9r^2-30r+9=0$

$9r^2-3r-27r+9=0$

$3r(3r-1)-9(3r-1)=0$

$(3r-9)(3r-1)=0$

⇒ $r=\frac{9}{3}=3,r=\frac{1}{3}$

Hence, the numbers are

when r=3: 3, 9, 27

when: $r=\frac{1}{3}$: 27, 9, 3

Hence, the three numbers are 3, 9, 27