Question

The sum of the three number is an ap is 9 and their product is 24 then number are

Answer 1

Answer:

2,3,4

Step-by-step explanation:

2+3+4=9

2×3×4=24

Answer 2

ANSWER :–

▪︎ Numbers are (2 , 3 , 4) or (4 , 3 , 2)

EXPLANATION :–

GIVEN :–

▪︎ The sum of the three number is an A.P. = 9

▪︎ Product of these three numbers = 24

TO FIND :–

Three numbers.

SOLUTION :–

▪︎ Let the numbers of A.P. are ⇨ (a - d) , a , (a + d)

▪︎ According to the question –

⮕ Sum of numbers = 9

⇒ (a - d) + a + (a + d) = 9

⇒ 3a = 9

⇒ a = 3

⮕ Product of numbers = 24

⇒ (a - d).(a)(a + d) = 24

• Now put the value of a –

⇒ (3 - d)(3)(3 + d) = 24

⇒ (3 - d)(3 + d) = 8

☞ We know that –

• (a - b)(a + b) = a² - b²

⇒ (3)² - (d)² = 8

⇒ 9 - (d)² = 8

⇒ (d)² = 1

⇒ d = 1 , d = -1

⮕ When a = 3 and d = 1 then numbers are ⇒ (2 , 3 , 4)

⮕ When a = 3 and d = -1 then numbers are ⇒ (4 , 3 , 2)

VERIFICATION :–

(1) When numbers are (2,3,4) :–

• Sum of numbers = 2+3+4 = 9 (Verified)

• Product of numbers = (2)(3)(4) = 24 (Verified)

(2) When numbers are (4,3,2) :–

• Sum of numbers = 4+3+2 = 9 (Verified)

• Product of numbers = (2)(3)(4) = 24 (Verified)