Question

The AM of two positive numbers is40 and their GM is 24.The numbers are

Answer 1

AM of a and b=a+b/2 and GM=√ab for any two numbers and AM,GM is Arithmetic and Geometric Means.AM of x and y be 40=> x+y/2=40=> x+y=80.
GM of x and y=√xy=24=>xy=576=> y=576/x.=> So we get x+576/x=80=> multiply by x=> we get
${x}^{2} + 576 = 80x = >$
${x}^{2} - 80x + 576 = 0 = >$ x^2-72x-8x+576=0
=> x(x-72)-8(x-72)=> (x-8)(x-72)=0=> x=72 and 8. So the numbers are 72 and 8.