Find the number in gp whose sum is 14 and whose product is 64
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Answered by
2
Answer:
Three numbers are 2 , 4 & 8
Step-by-step explanation:
Let say three numbers of GP are
a/r , a , ar
where a/r is 1st term of GP
and r is common ration
Then product of three term of GP will be
(a/r)(a)(ar) = 64
a³ = 64
a =∛64
a = 4
so three terms are
4/r , 4 , 4r
Sum of three terms = 14
4/r + 4 + 4r = 14
=> 4 + 4r + 4r² = 14r
=> 4r² - 10r + 4 = 0
=> 2r² - 5r + 2 = 0
=> 2r² - 4r - r + 2 = 0
=> 2r(r -2) -1(r-2) = 0
=> (2r -1)(r-2) = 0
=> r = 1/2 & r = 2
three terms are
4/r , 4 & 4r
8 , 4 , 2 (when r = 1/2)
2 , 4 , 8 (when r =2)
Answered by
1
Answer:
what
Step-by-step explanation:
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