Question

if the number (3x+2)(2x+3) and (2x-5) are in AP then the value of x​

Answer 1

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✝️ Required Answer:

✏ GiveN:

• (3x +2), (2x + 3) and (2x -5) are in AP

✏ To finD:

• Find the value of x ......?

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✝️ How to solve?

In an AP, the consecutive terms have an common difference. It is a successive additive series in which common difference is always same for consecutive terms.

• Let a, b and c are in AP

❇ Then, b - a = c - b

➙ b + b = a + c

➙ 2b = a + c

So, here we can say that, twice the second term = sum of first and third term in the series. Or the second term is the average of the first and third term.

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✝️ Solution:

Let,

• a = 3x + 2
• b = 2x + 3
• c = 2x - 5

Then, On the basis of above relation,

➙ 2(2x + 3) = 3x + 2 + 2x - 5

➙ 4x + 6 = 5x - 3

➙ 5x - 4x = 6 + 3

➙ x = 9

Verification:

If x = 9, then

• a = 3(9) + 2 = 29
• b = 2(9) + 3 = 21
• c = 2(9) - 5 = 13

Here, b - a = c - b = - 8, common difference.

So, a, b and c are in AP. (Verified!)

$\large{ \therefore{ \underline{ \underline{ \rm{ \pink{ Hence \: solved \: \dag}}}}}}$

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Answer 2

$\huge\bigstar\blue{Answer}$

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Here,

1st term is ( 3x + 2 )

2nd term is ( 2x + 3 )

3rd term is ( 2x - 5 )

Common difference ( d ) = >

( 2x + 3 ) - ( 3x + 2 ) = ( 2x - 5 ) - ( 2x + 3 )

= = > 2x + 3 - 3x - 2 = 2x - 5 - 2x - 3

= = > 2x - 3x + 3 - 2 = 2x - 2x - 5 - 3

= = > 1 - x = - 8

= = > x = 9

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VERIFICATION :-

( 3x + 2 ) = > 3(9) + 2 => 27 + 2 = 29

( 2x + 3 ) = > 2(9) + 3 => 18 + 3 => 21

( 2x - 5 ) = > 2(9) - 5 => 18 - 5 = 13

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21 - 29 = 13 - 21 = - 8

These are in AP ..........