Question

if the am and GM for two numbers are 6.5 and 6 respectively then the two numbers are​

Answer 1

Answer:9 and 4

Step-by-step explanation:

Answer 2

Given,

A.M. of two numbers = 6.5

G.M. of two numbers = 6

To Find,

Two numbers =?

Solution,

Let the two numbers be x and y

According to the formula of A.M., we know

A.M. = (x + y) / 2 = 6.5

(x + y)  = 6.5 * 2

x + y = 13 ⇒ Equation 1

According to the formula of A.M., we know

G.M. = $\sqrt{xy} = 6$

Squaring both sides, we get

xy = 36

y = 36 / x ⇒ Equation 2

Putting the value of y from equation 2 in equation 1,

$x + \frac{36}{x} = 13\\\frac{x^2 + 36 }{x} = 13\\x^2 + 36 = 13x\\x^2 - 13x +36 = 0$

$x^2 - 9x - 4x +36 = 0\\x(x - 9) -4(x - 9) = 0\\(x-9)(x - 4) = 0$

x = 9 or 4

if x = 9 , y = 36 / 9 = 4

if x = 4 , y = 36 / 4 = 9

Hence, if the am and GM for two numbers are 6.5 and 6 respectively then the two numbers are​ 4,9