Question

Three numbers are in gp. their sum is 28 and product is 512. the number are

Answer 1

let nos be a/r ,a, ar
product is 512
a*a*a=512
a=8
a/r)+a+ar=28
put a=8,then find r... and u will get numbers

Answer 2

The three numbers in GP are 4 , 8 , 16.

• Let the three numbers in GP be a/r , a , ar.
• Now the product of three numbers is given as 512.

a/r × a × ar = 512

a³ = 512

a = 8

• Now sum of the three numbers is given as 28.

a/r + a + ar = 28

8/r + 8 + 8r = 28

8 + 8r² = 20r

8r² - 20r + 8 =0

8r² - 16r - 4r + 8 =0

8r(r-2) - 4(r-2) = 0

(r-2)(8r-4) = 0

• Therefore, r = 2 or r=1/2
• Now , the  three numbers are 4,8,16.