Question

The three numbers in g.p whose sum is 21 and whose product is 216​

Answer 1

Answer:

The three no. are 12, 6 and 3.

Step-by-step explanation:

The three no. are 12, 6 and 3, if we add then it becomes 21 and multiply then It becomes 216.

Total no. which have the sum of 21 and product of 216 = 3

Then, 216÷3=72.

: and the double of 3 is equal to 6. and then, 72 ÷ 6=12

now, 12 + 6 + 3 = 21.

and 12 × 6 × 3 = 216.

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Answer 2

Answer:

3, 6, 12 or 12, 6, 3

Step-by-step explanation:

Let the three numbers in GP be (a/x), (a) and (ax).

According to question,

(a/x) + (a) + (ax) = 21 ------------ (1)

Also, according to the question,

(a/x) * (a) * (ax) = 216

=> a * a * a = 216

=> a³ = 216

=> a = $\sqrt[3]{216}$

=> a = 6

Substituting the value of 'a' in the equation (1),

(6/x) + 6 + (6x) = 21

(6/x) + 6x = 21 - 6

(6x² + 6)/x = 15

6x² + 6 = 15x

6x² - 15x + 6 = 0

6x² - 12x - 3x + 6 = 0

6x(x - 2) - 3(x - 2) = 0

(x - 2 ) (6x - 3) = 0

3 (x - 2) (2x - 1) = 0

(x - 2) (2x - 1) = 0

By zero product rule,

x = 2 or x = 1/2

When x = 2,

Three numbers = 3, 6, 12

When x = 1/2,

Three numbers = 12, 6, 3