Question

the sum of three numbers in arithmetic progression is 15 and there product is 120 find the numbers​

Answer 1

$\large \underline{ \underline{ \sf \: Solution : \: \: \: }}$

Let ,

The three numbers = a - d , a , a + d

According to the question ,

Sum of the numbers is 15

$\to \sf a - d + a + a + d = 15</p><p> \\ \\ \to \sf </p><p>3a = 15 </p><p> \\ \\ \to \sf </p><p>a = 5</p><p>$

Product of the numbers is 120

$\to \sf (a - d) × (a) × (a + d) = 120 \\ \\ \to \sf</p><p></p><p> ( {a}^{2} - {d}^{2} ) × a = 120</p><p> \\ \\ \to \sf</p><p>25 - {d}^{2} = 24</p><p> \\ \\ \to \sf</p><p>- {d}^{2} = -1</p><p> \\ \\ \to \sf </p><p>d = 1$

Therefore , the required numbers are 4 , 5 , 6