Question

find three numbers in A.P. whose sum is 24 and whose product is 480?

Answer 1

Hey there !!

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

▶Now,

A/Q,

=> ( a - d ) + a + ( a + d ) = 24.

=> a - d + a + a + d = 24.

=> 3a = 24.

=> a = 24/3.

=> a = 8.

And,

=> ( a - d )× a× ( a + d )= 480.

=> (a - d ) ×8 × ( a + d ) = 480.

=> a² - d² = 480/8.

=> 8² - d² = 60.

=> 64 - d² = 60.

=> d² = 64 - 60.

=> d² = 4.

=> d = √4.

=> d = ±2.

▶ When taking, a = 8 and d = 2, we get

→ a - d = 8 - 2 = 6.

→ a = 8.

→ a + d = 8 + 2 = 10.

And, when taking, a = 8 and d = -2, we get

→ a - d = 8 - (-2) = 8 + 2 = 10.

→ a = 8.

→ a + d = 8 + (-2) = 8 - 2 = 6.

✔✔ Hence, the required number are ( 6, 8, 10 ) or ( 10, 8, 6 ). ✅✅

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