The product of three consecutive terms of a G.P. is 64. The sum of product of numbers taken in pair is 56. Find the numbers.

Answer

N/a

Explanation

Let three consecutive terms in G.P. be `(a)/(r),a,ar.`
`therefore" "(a)/(r)cdotacdotar=64`
`rArr" "a^(3)=64`
`rArr" "a=4`
`rArr" "a=4`
`"and "(a)/(r)cdota+acdotar+(a)/(r).ar=56`
`rArr" "(16)/(r)+16r+16=56`
`rArr" "2r+(2)/(r)-5=0`
`rArr" "2r^(2)-5r+2=0`
`rArr" "(r-2)(2r-1)=0`
`rArr" "r=2`
`"or "r=(1)/(2)`
`a=4,r=2,"then numbers are 2, 4, 8."`
`a=4,r=(1)/(2),"then numbers are 8, 4, 2."`