Question

find three numbers in AP whose sum is 24 and product is 440

Answer 1

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here is your answer

Solution

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Let the three numbers in ap be

a - d, a , a + d

Sum of three number is 24

( a - d ) + ( a ) + ( a + d ) =24.

a + a + a - d + d = 24

3a + 0 = 24

a = 24
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3

hence a = 8
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also given product of three number is 440

( a - d ) * ( a ) * ( a + d ) = 440

( a - d ) ( a + d )a = 440

( a^2 - d^2 ) a = 440

putting a = 8

( 8^2 - d ^2 ) 8 = 440

8^2 - d^2 = 440
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8

64 - d^2 = 55

64 - 55 = d^2

9 = d ^2

+-√9 = d

hence d = 3

hence answer is d = +3 & d = -3

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hope it helps

thank you