Question

find the three numbers in AP whose sum is 15 and their product is 105​

Answer 1

Let the numbers be a-d, a, a+d

Sum of the numbers = 15 = a-d+a+a+d

3a = 15

a = 5

Product of numbers = 105 = a(a-d)(a+d)

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

25-d² = 21

d²=4

d=±4

Therefore we get two APs,

If d=4, If d=-4

AP=5,9,13......... AP=5,1,-3.............

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Answer 2

Answer:

Step-by-step explanation:

Let the numbers be a-d, a, a+d

Sum of the numbers = 15 = a-d+a+a+d

3a = 15

a = 5

Product of numbers = 105 = a(a-d)(a+d)

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

25-d² = 21

d²=4

d=±2

Therefore we get two APs,

If d=2     AP=  3.5.7......  

If d= -2     AP=  7.5.3....