Find four numbers is G.P. such that thpeir product is 64 and sum of the second and third number is 6.
Answers
EXPLANATION.
Fourth term are in Gp their products is 64
and the sum of second and third number
is 6
Find four number in Gp.
According to the question,
Let the Four terms in Gp = a, b, c, d
sum of second and third is = 6
=> b + c = 6 ..... (1)
as we know that,
conditions of an Gp
=> b² = ac = a = b²/c
=> c² = bd = d = c²/b
Sum of their products is 64
=> a X b X c X d = 64
=> b²/c X b X c X c²/b = 64
=> b²c² = 64
=> bc = √64
=> bc = 8
From equation (1) we get,
=> c = 6 - b
we get,
=> b ( 6 - b) = 8
=> 6b - b² = 8
=> b² - 6b + 8 = 0
=> b² - 4b - 2b + 8 = 0
=> b ( b - 4 ) -2 ( b - 4 ) = 0
=> ( b- 2 ) ( b - 4 ) = 0
=> b = 2 and b = 4
when b = 2
=> c = 6 - 2 = 4
=> a = b²/c = 4/4 = 1
=> d = c²/b = 16/2 = 8
We get, = 1,2,4,8 .......
when b = 4
=> c = 6 - 4 = 2
=> a = b²/c = 16/2 = 8
=> d = c²/b = 4/4 = 1
we get, = 8,4,2,1.....