Question

Arithmetic means between two numbers is 10 and geometric mean is 8 find the numbers

Answer 1

Answer:

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Step-by-step explanation:

Let the no. be x and y

Arithmetic means = x+y / 2 = 10'

x + y = 20

Geometric mean = $\sqrt{xy}$ = 8

xy = 64

x = $\frac{64}{y}$

putting x = 64/y in x + y = 20

$\frac{64}{y}$ + y = 20

$y^{2}$ - 20y + 64 = 0

Solving the above equation , we rget

y = 4 / 16

putting valur if y in x + y = 20, we get

x = 16/4

∴ The numbers are 4 and 16

Answer 2

the number be x,y
2
x+y
​
=A........(1)
xy
​
=G⇒y=
x
G
2

​

putthevalueof
′
y
′
inequation(1)
2
x+
x
G
2

​

​
=A
x
2
+G
2
=2Ax
x
2
−2Ax+G
2
=0
x=
2
2A±
4A
2
−4G
2

​

​

x=A±
A
2
−G
2

​

​