Question

The sum of two numbers is equal to 15 and their arithmetic mean is
25 per cent greater than their geometric mean. Find the numbers.​

Answer 1

Answer:

Step-by-step explanation:

First of all you need to know the difference between arithemetic mean and geometric mean

Let the first number be x

Let the second number be y

Arithemetic Mean = ( x+y ) /2

Geometric Mean = $\sqrt{xy}$

According to the question

x + y = 15

y = 15 - x               - ( 1 )

Also

AM is 25% greater than their GM

( x + y )/2 = 0.25 x $\sqrt{xy}$ + $\sqrt{xy}$

( x + y ) = $\sqrt{xy}$ ( 0.50 + 1 )

( x + y ) = $\sqrt{xy}$ ( 1.50 )

Put value of y from equation number ( 1 )

( x + 15 - x ) = $\sqrt{x(15-x)}$ (1.5)

15 / 1.5= $\sqrt{15x-x^{2} }$

10 = $\sqrt{15x-x^{2} }$

squaring both the sides we get

$100 = 15x - x^{2}$

$x^{2} - 15x +100 = 0$