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If the continued product of three numbers in G.P. is 27 and the sum of their products in pairs is 39 the numbers are_______.
- a)1, 3, 9
- b)9, 3, 1
- c)Both
- d)None
Correct answer is option 'C'. Can you explain this answer?
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If the continued product of three numbers in G.P. is 27 and the sum of...
Given, the continued product of three numbers in G.P. is 27.
Let the numbers be a/r, a, ar.
Then, (a/r) * a * ar = 27
=> a^3 = 27r^2
=> a = 3r
Also, the sum of their products in pairs is 39.
=> (a/r * a) + (a/r * ar) + (a * ar) = 39
=> a^2 (1/r + r) = 39
Substituting a = 3r, we get
=> 9r^2 (1/r + r) = 39
=> 9r^2 + 9 = 39r
=> 9r^2 - 39r + 9 = 0
=> (3r-1)(3r-3) = 0
=> r = 1/3 or r = 3
Therefore, the numbers are either 1, 3, 9 or 9, 3, 1.
Hence, option C (Both) is the correct answer.
Let the numbers be a/r, a, ar.
Then, (a/r) * a * ar = 27
=> a^3 = 27r^2
=> a = 3r
Also, the sum of their products in pairs is 39.
=> (a/r * a) + (a/r * ar) + (a * ar) = 39
=> a^2 (1/r + r) = 39
Substituting a = 3r, we get
=> 9r^2 (1/r + r) = 39
=> 9r^2 + 9 = 39r
=> 9r^2 - 39r + 9 = 0
=> (3r-1)(3r-3) = 0
=> r = 1/3 or r = 3
Therefore, the numbers are either 1, 3, 9 or 9, 3, 1.
Hence, option C (Both) is the correct answer.
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If the continued product of three numbers in G.P. is 27 and the sum of...
Answer is option C
chech each option whether these are satisfied condition or not
chech each option whether these are satisfied condition or not
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If the continued product of three numbers in G.P. is 27 and the sum of their products in pairs is 39 the numbers are_______.a)1, 3, 9b)9, 3, 1c)Bothd)NoneCorrect answer is option 'C'. Can you explain this answer?
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