Question

The arithmatic mean of two nos is 10 and the gemotric mean is 8then two nos are

Answer 1

Call the numbers x and y. Then  

(x + y)/2 = 10 <----arithmetic mean  

√(xy) = 8 <---- geometric mean.  

These equations can be stated as  

x + y = 20, and xy = 64.  

Now you have two equations in two unknowns. You can use some substitution to solve.  

y = 20 - x ==> x(20 - x) = 64 ==> x² - 20x + 64 = 0 ==> (x - 4)(x - 16) = 0  

Giving x = 4 or x = 16. This gives one pair of numbers (x = 4 y = 16 or x = 16 y = 4.)