Question

Find the three numbers of G.P such that the respective sum and product are 6 and -64​

Answer 1

Step-by-step explanation:

Let the three numbers be a/r,a,ar

⇒a/r×a×ar=1000

⇒a3=1000

⇒a=10

2(a+6)=(ar+7)+a/r where a=10

⇒32r=10r 2+7r+10

⇒10r2+7r−32r+10=0

⇒10r2−25r+10=0

⇒2r2−5r+2=0

⇒2r2−4r−r+2=0

⇒2r(r−2)−1(r−2)=0

⇒(r−2)(2r−1)=0

⇒r=2 1/2

∴a=10,r=2⇒ terms are

10/2,10,10×2 or 5,10,20

∴a=10,r=1/2⇒ terms are 10/1/2 ,10,10×1/2or 20,10,5