Question

Find three numbers in an ap whose sum and product is 21and 343 respectively

Answer 1

Answer:

• Three numbers are (7, 8 and 6) and (7, 6 and 8).

Step-by-step explanation:

Let three number be 'a', 'a + d' and 'a - d'.

Given:

• Sum of three numbers = 21
• Product of three numbers = 343

To Find:

• Three numbers.

So, it is given sum of three numbers be 21.

⇒ a + a + d + a - d = 21

⇒ 3a = 21

⇒ a = 21/3

⇒ a = 7

And product of three numbers be 343

⇒ a × (a + b) × (a - b) = 343

⇒ a × (a² - d²) = 343

Now, put the value of a, we get

⇒ 7 × (49 × d²) = 343

⇒ 49 × d² = 343/7

⇒ 49 × d² = 49

⇒ d² = 1

⇒ d = ± 1

Now, numbers are:

First we will take d = 1

• a = 7
• a + d = 7 + 1 = 8
• a - d = 7 - 1 = 6

Now, d = -1

• a = 7
• a + d = 7 - 1 = 6
• a - d = 7 + 1 = 8

Hence, three numbers are (7, 8 and 6) and (7, 6 and 8).

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