The sum of three numbers in GP is 39 10 and their product is 1 . Find the numbers.

Let the first three numbers in GP be a r , a , a r By the given data, a r + a + a r = 39 10 . . . . . 1 and a r × a × a r = 1 ⇒ a 3 = 1 ⇒ a = 1 Substitute the value of a in the equation 1 ⇒ 1 r + 1 + r = 39 10 ⇒ 1 + r + r 2 r = 39 10 ⇒ 10 1 + r + r 2 = 39 r ⇒ 10 + 10 r + 10 r 2 = 39 r ⇒ 10 r 2 - 29 r + 10 = 0 ⇒ 10 r 2 - 25 r - 4 r + 10 = 0 ⇒ 5 r 2 r - 5 - 2 ( 2 r - 5 ) = 0 ⇒ 2 r - 5 5 r - 2 = 0 ⇒ r = 5 2 , 2 5 When a = 1 and r = 5 2 , ⇒ The three numbers are 2 5 , 1 , 5 2 When a = 1 and r = 2 5 ⇒ The three numbers are 5 2 , 1 , 2 5

The sum of first three terms of a GP is 13 12 and their product is -1 . Find the GP

Let the first three numbers in GP be a r , a , a r By the given data, a r + a + a r = 13 12 . . . . . 1 and a r × a × a r = - 1 ⇒ a 3 = - 1 ⇒ a = - 1 Substitute the value of a in the equation 1 ⇒ - 1 r - 1 - r = 13 12 ⇒ 1 + r + r 2 r = - 13 12 ⇒ 12 1 + r + r 2 = - 13 r ⇒ 12 + 12 r + 12 r 2 = - 13 r ⇒ 12 r 2 + 25 r + 12 = 0 ⇒ 12 r 2 + 16 r + 9 r + 12 = 0 ⇒ 4 r 3 r + 4 + 3 ( 3 r + 4 ) = 0 ⇒ 3 r + 4 4 r + 3 = 0 ⇒ r = - 4 3 , - 3 4 When a = - 1 and r = - 4 3 , ⇒ The three numbers are 3 4 , - 1 , 4 3 When a = - 1 and r = - 3 4 ⇒ The three numbers are 4 3 , - 1 , 3 4

E M B I B E

Senior Secondary School Mathematics FOR CLASS 11>Algebra>Chapter 12 - Geometrical Progression>EXERCISE 12B

R S Aggarwal Solutions for Exercise 2: EXERCISE 12B

Author:R S Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal Solutions for Exercise 2: EXERCISE 12B

Attempt the practice questions from Exercise 2: EXERCISE 12B with hints and solutions to strengthen your understanding. Senior Secondary School Mathematics FOR CLASS 11 solutions are prepared by Experienced Embibe Experts.

Questions from R S Aggarwal Solutions for Exercise 2: EXERCISE 12B with Hints & Solutions

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 12 - Geometrical Progression>EXERCISE 12B>Q 2

For what values of $x$ are the numbers $(x + 9), (x - 6)$ and $4$ in GP?

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 12 - Geometrical Progression>EXERCISE 12B>Q 3

The sum of three numbers in GP is $\frac{39}{10}$ and their product is $1$ . Find the numbers.

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 12 - Geometrical Progression>EXERCISE 12B>Q 4

The sum of first three terms of a GP is $\frac{13}{12}$ and their product is $-1$ . Find the GP

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 12 - Geometrical Progression>EXERCISE 12B>Q 5

Find three numbers in GP whose sum is $38$ and whose product is 1728.

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 12 - Geometrical Progression>EXERCISE 12B>Q 6

Find three numbers in GP whose sum is $65$ and whose product is 3375.

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 12 - Geometrical Progression>EXERCISE 12B>Q 7

The sum of three numbers in GP is $21$ and the sum of their squares is $189$ . Find the numbers.

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 12 - Geometrical Progression>EXERCISE 12B>Q 8

The product of three numbers in GP is $216$ . If $2, 8, 6$ be added to them in that order, we get an AP. Find the numbers.

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 12 - Geometrical Progression>EXERCISE 12B>Q 9

The product of three numbers in GP is $1000$ . If $6$ is added to the second number and $7$ is added to the third number, we get an AP. Find the numbers.

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