Find the three numbers in G.P. such that their sum is 13/3 and the sum of their squares is 91/3.
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Answered by
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● LET'S THE THREE NUMBERS ARE
=> [a, ar, and ar²]
______________________________
◢NOW,
● ACCORDING TO THE QUESTION
◢AND
________________________________
◢NOW,
_________________________________
● WE KNOW THAT..
=> (A+B+C)²
= (A²+B²+C²+2AB+2BC+2CA)
_________________________________-
● USING THIS IDENTITY FOR Eq(3)
◢WE GET,
_________________________________
● NOW TAKE :- [Eq(4) - Eq(2)]
_______________________________
● USING Eq(1) AGAIN
◢SO
______________________________
● BY Eq(1) AND Eq(5)
_______________________________
◢THEN
◢OR
_______________________________
◢IF "a = 1/3"
◢THEN
◢and
◢IF "a = 3"
◢THEN
______________________________
◢THEN
๏ CONDITION 1ST
◢IF "a=3" and "r=1/3"
● THE NUMBER OF GP ARE
=> 3, 1, 1/3
______________[◢ANSWER]
๏ CONDITION 2ND
◢IF "a=1/3" AND "r=3"
● THE NUMBER OF GP AER
=> 1/3, 1, 3
______________[◢ANSWER]
=============================
☆BE BRAINLY☆
=> [a, ar, and ar²]
______________________________
◢NOW,
● ACCORDING TO THE QUESTION
◢AND
________________________________
◢NOW,
_________________________________
● WE KNOW THAT..
=> (A+B+C)²
= (A²+B²+C²+2AB+2BC+2CA)
_________________________________-
● USING THIS IDENTITY FOR Eq(3)
◢WE GET,
_________________________________
● NOW TAKE :- [Eq(4) - Eq(2)]
_______________________________
● USING Eq(1) AGAIN
◢SO
______________________________
● BY Eq(1) AND Eq(5)
_______________________________
◢THEN
◢OR
_______________________________
◢IF "a = 1/3"
◢THEN
◢and
◢IF "a = 3"
◢THEN
______________________________
◢THEN
๏ CONDITION 1ST
◢IF "a=3" and "r=1/3"
● THE NUMBER OF GP ARE
=> 3, 1, 1/3
______________[◢ANSWER]
๏ CONDITION 2ND
◢IF "a=1/3" AND "r=3"
● THE NUMBER OF GP AER
=> 1/3, 1, 3
______________[◢ANSWER]
=============================
☆BE BRAINLY☆
Swarup1998:
Nicely answered! :clap:
Answered by
1
Answer:
the answer is 3,1,1/3
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