The product of 3 numbers in g.p is 729 and sum of squares is 819
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Hello Aditya
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.
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.
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