Question

Find three numbers in A.P. whose sum is 15 and whose product is 105

Answer 1

Let the ap be x, y and z

x+y+z=15

xyz=105

the nunbers are in the form of a-d,a,a+d(a is the first term ,d is the common diffrence)

x+y+z=a-d+a+a+d=3a=15

⇒a=5

xyz=(a-d)(a+d)a=(a-d)^2*a=(a^2-d^2)a=105

substuting the value of a we get ...

(5^2-d^2)5=25-d^2=21

d^2=25-21=4

d=⌈4=2

⇒the terms are

5-2,5,5+2=3,5,7

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Answer 2

Let the numbers are:

a-d, a, a+d (An A. P.)

Sum = 15

a-d + a + a+d = 15

3a = 15

a = 5

Product = 105

(a-d) x 5 x (a+d) = 105

(a-d) x (a+d) = 105/5

a² - d² = 21

25 - d² = 21

d²= 4

d = 2

The numbers are 3, 5, 7

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