Question

Find the sum of three numbers in an AP is 27 and their product is 405 the numbers are

plz give step by step EXPLANATION​

Answer 1

GiveN :

• Sum of three numbers in an AP is 27. and their product is 405.

To FinD :

The number.

SolutioN :

Let,

• a - d , a , a + d are in AP.

$\rule{90}2$

☛ Case 1.

• Sum of three numbers in an AP is 27.

→ a - d + a + a + d = 27.

→ 3a = 27.

→ a = 27/3.

→ a = 9.

$\rule{90}2$

☛ Case 2.

• Their product is 405.

→ ( a - d )( a )( a - d ) = 405.

→ a² - d² ( a ) = 405.

→ 9² - d² = 405/9.

→ 81 - d² = 45.

→ - d² = 45 - 81.

→ - d² = - 36.

→ d² = 36.

→ d = ± 6.

$\rule{90}2$

• When, a = 9 and, d = 6.
• a - d , a , a + d.
• 9 - 6 , 9 , 9 + 6.
• 3 , 9 , 15.

$\rule{90}2$

• When, a = 9 and, d = - 6.
• a - d , a , a + d.
• 9 + 6 , 9 , 9 - 6.
• 15 , 9 , 3.

Therefore, the three number is 3 , 9 , 15.