Question

Find the two number whose A.M is 5 and G.M is 4​

Answer 1

2 and 8

Explanation:

let the numbers be x and y , then

`(x+y)/(2)` = 5 ( multiply both sides by 2 ) ← AM

x + y = 10 → (1)

`√(xy)` = 4 ( square both sides ) ← GM

xy = 16 → (2)

From (1) , expressing x in terms of y

x = 10 - y ← substitute into (2)

(10 - y)y = 16

10y - y² = 16 ( subtract 16 from both sides )

10y - y² - 16 = 0 ( multiply through by - 1 )

y² - 10y + 16 = 0 ← in standard form

(y - 2)(y - 8) = 0 ← in factored form

Equate each factor to zero and solve for y

y - 2 = 0 ⇒ y = 2

y - 8 = 0 ⇒ y = 8

Substitute into (1)

x + 2 = 10 ⇒ x = 8 or x + 8 = 10 ⇒ x = 2

The 2 numbers are 2 and 8