Question

8 The lan their sum of Anthmetic Product is three numbers in progression is 12 and 40 find there numbars ​

Answer 1

Step-by-step explanation:

Let 3 numbers in A.P. be (a - d), a, (a + d)

→ Sum of 3 numbers = 12

a-d+a+a+d=12

3a = 12

a = 4

sum of their cubes = 408

(a −d)³ + a³ + (a + d)³ = 408

a³d³-3a²d +3ad² + a³ + a²³ +d³ + 3a²d + 3ad² = 408

3a³ + 6ad² = 408

aº +2ad² = 136

(4)³ + 2 (4) d² = 136

8d² = 136 64

8d² = 72

d² = 9

d = ±3

d = 3,

series 4-3, 4,4+3 ⇒ 1,4,7 series 4-(),4,4-3

⇒ 7,4,1

d = -3,

..3 numbers are 1,4 and 7.