Question

The sum of three numbers in ap is 36 and their product is 1140

Answer 1

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Answer 2

The three numbers in A.P are 5,12,19.

Step-by-step explanation:

Given : The sum of three numbers in AP is 36 and their product is 1140.

To find : The three numbers in AP ?

Solution :

Let the three numbers in A.P be (a-d), a and (a+d) respectively.

The sum of three numbers in AP is 36.

$a-d+a+a+d=36$

$3a=36$

$a=\frac{36}{3}$

$a=12$

Product of three numbers is 1140.

$(a-d)\times(a)\times (a+d)=1140$

$a(a^2-d^2)=1140$

$12(12^2-d^2)=1140$

$144-d^2=\frac{1140}{12}$

$144-d^2=95$

$d^2=144-95$

$d^2=49$

$d=\sqrt{49}$

$d=\pm 7$

When a=12 and d=7,

a-d=12-7=5

a=12

a+d=12+7=19

When a=12 and d=-7,

a-d=12-(-7)=19

a=12

a+d=12-7=5

Therefore, the three numbers in A.P are 5,12,19.

#Learn more

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