Question

the sum of 3 terms in Gp is 14 & their product is 64, find them

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Answer 1

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)