Question

the sum of three numbers in A.P is 15 and the sum of their square is 93 find the numbers
it is very urgent

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Answer 1

Answer:

9.5

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Answer 2

Solution:-

let the required number be ( a - d ) , a and ( a + d )

The sum of three number is 15

⇒ a - d + a + a + d =15

⇒ 3a = 15

⇒ a = 15/3

⇒a = 5

The product of three number is 93

⇒a . ( a - d ) . ( a + d ) = 93

⇒a ( a² - d² ) = 93

when a = 5

⇒ 5 ( 5² - d² ) = 93

⇒ 5 ( 25 - d² ) = 93

⇒ 125 - 5d² = 93

⇒ - 5d² = 93 - 125

⇒ - 5d² = - 32

⇒ 5d² = 32

⇒ d = ±√32/5

Thus a = 5 and d = ±√32/5

Hence required number ( 5 + √32/5 ) , 5 , ( 5 - √32/5 ) and  ( 5 - √32/5 ) , 5 , ( 5 + √32/5 )