Split 207 into three parts such that these are in AP and the product o

1.	Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623.
Answer» Let the three parts of the number 207 are a₁ = a - d a₂ = a a₃ = a + d Clearly a₁, a₂ and a₃ are in AP with common difference as d. Now, by given condition, Sum = 207 a₁ + a₂ + a₃ = 207 (a - d) + a + (a + d) = 207 3a = 207 a = 69 Also, a₁a₂ = 4623 (a - d)a = 4623 (69 - d)69 = 4623 69 - d = 67 d = 69 - 67 d = 2 Hence, required three parts are 67, 69, 71.

Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623.

Answer»

Let the three parts of the number 207 are

a₁ = a - d

a₂ = a

a₃ = a + d

Clearly a₁, a₂ and a₃ are in AP with common difference as d.

Now, by given condition,

Sum = 207

a₁ + a₂ + a₃ = 207

(a - d) + a + (a + d) = 207

3a = 207

a = 69

Also,

a₁a₂ = 4623

(a - d)a = 4623

(69 - d)69 = 4623

69 - d = 67

d = 69 - 67

d = 2

Hence, required three parts are 67, 69, 71.