Question

step by step plz ans fast this is the question for 10th

find three numbers in gp such that their sum and product are respectively 14and64​

Answer 1

Answer:

8,2,4

Step-by-step explanation:

8+2+4=14

8×2×4=64

Answer 2

Step-by-step explanation:

Given:-

three numbers in gp such that their sum and product are respectively 14and64

To find:-

find the three terms in the GP

Solution:-

Let the three terms in the GP are a/r;a;ar

their sum=(a/r)+a+ar=14

=>(a+ar+ar²)/r=14

=>a+ar+ar²=14r-----(1)

Their product=64

=>(a/r)(a)(ar)=64

=>(a)(a)(a)=64

=>a³=64

=>a³=4³

=>a=4-----(2)

from (1)

=>4+4r+4r²=14r

=>4r²+4r-14r+4=0

=>4r²-10r+4=0

=>4r²-8r-2r+4=0

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

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

4r-2=0 or r-2=0

=>r=2/4 or r=2

=>r=1/2 or 2-----(3)

a=4

ar=4(2) or4(1/2)

=>ar=8 or 2

a/r=4/2 or 4/(1/2)

=>a/r=2 or 8

The three terms are 2,4,8

Answer:-

The three terms are 2,4,8 in the given GP