Question

The arithmetic mean between two numbers is and their geometric mean is 21. Find the numbers:

• A. 100, 44.5
• B. 147,3
• C. 126, 6
• D. 98, 4.5

Answer 1

Answer:

B. 147,3

$AM=(a+b)/2=75$

$a+b=150$

$GM=\sqrt{ab}=21$

$ab=21^2=441$

$(a-b)^2=(a+b)^2-4ab$

$=150^2-4\times441$

$=20736$

$a-b=144$

2a=294\implies{a}=147$</p><p style="color: rgb(0,0,0); margin-top: 2px; margin-bottom: 2px" data-pxy="true">$b=3$