Question

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

Answer 1

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.