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The Sum of Three Nu,Bers in G.P is and Their Product is 1. Find the Numbers. - Mathematics

Sum

The sum of three nu,bers in G.P is `39/10` and their product is 1. Find the numbers.

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Solution

Let the number be `a/r`, a and ar.

⇒ `a/r xx a xx ar = 1`

⇒ a3 = 1

⇒ a = 1

Now, `a/r+a+ar=39/10`

⇒ `1/r+1+r=39/10`

⇒ `(1+r+r^2)/r=39/10`

⇒ 10 + 10r + 10r2 = 39r

⇒ 10r2 - 29r + 10 = 0

⇒ 10r2 - 25r - 4r + 10 = 0

⇒ 5r(2r - 5) - 2(2r - 5) = 0

⇒ (2r - 5)(5r - 2) = 0

⇒ r = `5/2` or r = `2/5`

Thus, required terms are :

`a/r, a, ar = 1/(5/2), 1, 1xx5/2` OR `1/(2/5), 1, 1xx2/5`

`=2/5, 1, 5/2`  Or  `5/2, 1, 2/5`

Concept: Simple Applications - Geometric Progression
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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 11 Geometric Progression
Exercise 11 (D) | Q 13 | Page 161
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