Question

the 3 no in a.P whom sum is 12 and product is 48​

Answer 1

Answer:

$\Large{\underline{\underline{\bf{QuEsTiOn:-}}}}$

Find the three numbers in A.P whose sum is 12 and product is 48.

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}</p><p>\mid}}}$

$\large{\underline{\boxed{\bf (2,4,6) \: or \: (6,4,2)}}}$

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Solve:- \: \star}}}}}$

Let the required numbers be (a - d), a and (a + d).

Let the required numbers be (a - d), a and (a + d). It is given that ;

Sum of numbers is 12

⇒ a - d + a + a + d = 12

⇒ 3a = 12

⇒ a = $\sf \dfrac{12}{3}$

⇒ a = 4

Also, the product of numbers is 48.

⇒ (a - d) * a * (a + d) = 48.

⇒ a (a² - d²) = 48

⇒ 4 (4² - d²) = 48

⇒ (16 - d²) = $\sf \dfrac{48}{4}$

⇒ 16 - d² = 12

⇒ d² = 16 - 12

⇒ d² = 4

⇒ d = ± √4

⇒ d = ± 2

Thus, a = 4 and d = ± 2.

The required numbers are;

(a - d) = (4 - 2) = 2

a = 4

(a + d) = 4 + 2 = 6

Or, the other possibility can be -

(a - d) = 4 + 2 = 6

a = 4

(a + d) = 4 - 2 = 2

$\mathfrak{\huge{\purple{\underline{\underline{Hence}}}}}$

The required numbers in an AP are (2, 4, 6) or (6, 4, 2).

Answer 2

$\boxed{ \tt{Question :}}$

→ Find three numbers in A.P. whose sum is 12 and product is 48.

$\boxed{ \tt{Answer :}}$

→ 2 , 4 αɳ∂ 6 .

$\boxed{ \tt{Explanation :}}$

→ Let the required numbers be (a - d), a and (a + d).

→ It is given that ,

→ Sum of numbers is 12

$\tt{⇒ a - d + a + a + d = 12}$

$\tt{⇒ 3a = 12}$

$\tt{⇒ a = \sf \dfrac{12}{3}}$

$\tt{⇒ a = 4}$

→ Also, the product of numbers is 48.

$\tt{⇒ (a - d) \times a \times (a + d) = 48.}$

$\tt{⇒ a (a² - d²) = 48}$

$\tt{⇒ 4 (4² - d²) = 48}$

$\tt{⇒ (16 - d²) = \sf \dfrac{48}{4} }$

$\tt{⇒ 16 - d² = 12}$

$\tt{⇒ d² = 16 - 12}$

$\tt{⇒ d² = 4}$

$\tt{⇒ d = ± √4}$

$\tt{⇒ d = ± 2}$

→ Thus, a = 4 and d = ± 2.

→ The required numbers are :

→ (a - d) = (4 - 2) = 2

→ a = 4

→ (a + d) = 4 + 2 = 6

→ Or, the other possibility can be -

→ (a - d) = 4 + 2 = 6

→ a = 4

→ (a + d) = 4 - 2 = 2

$\tt \pink{♡ \: Hope \: it \: helps \: ♡}$