Question

Find three numbers in ap whosr sum is 9and the product is 165

Answer 1

Answer:

3 - ι√46,  3,  3 + ι√46

Step-by-step explanation:

Let the three terms be a, a + d and a + 2d.

⇒ Sum of terms = 9

⇒ a + a + d + a + 2d = 9

⇒ 3a + 3d = 9

⇒ 3(a + d) = 9

⇒ a + d = 3

Thus the second term is 3. In respect to this,

a = a + d - d = 3 - d

a + 2d = a + d + d = 3 + d

⇒ Product of terms = 165

⇒ a(a + d)(a + 2d) = 165

⇒ (3 - d) 3 (3 + d) = 165

⇒ 3(3 - d)(3 + d) = 165

⇒ 3(9 - d²) = 165

⇒ 9 - d² = 165 / 3

⇒ 9 - d² = 55

⇒ 9 - 55 = d²

⇒ -46 = d²

⇒ d = ±√-46

⇒ d = ±ι√46

Taking d = ι√46,

⇒ a = 3 - ι√46

⇒ a + 2d = 3 + ι√46

Taking d = -ι√46,

⇒ a = 3 + ι√46

⇒ a + 2d = 3 - ι√46

Thus the three numbers are 3 - ι√46, 3 and 3 + ι√46.