Question

The product of three numbers in gp is 729 and the sum of squares

Answer 1

Step-by-step explanation:

hello

ans in attachment

Answer 2

Let the numbers in GP be a/r,a and ar where r is common ratio of the GP.

Then According to question

a/r×a ×ar=729

or,a³=729

or,a=9

Now since the sum of their squares is 819

Therefore

(a/r)²+a²+(ar)²=819

or,a²(1/r²+1²+r²)=819

or,9²(r^4+r²+1)/r²=819

or,(r^4+r²+1)/r²=10

or,(r^4+r²+1)=10r²

or,r^4-9r²+1=0

let r²=t

then

t²-9t+1=0

or,t=9 or t=0   (approximately)

or r²=9

or,r=3

Hence the gp is

9/3,9,9x3

or,3,9,27

Hope it Helps.