SOLUTION: If m : n is the duplicate ratio of m + x : n + X show that: x^2 = mn. Unable to solve please help

Question 1086608: If m : n is the duplicate ratio of m + x : n + X show that: x^2 = mn.
Unable to solve please help
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Using the definition of Duplicate Ratio, we can say that m/n is equal to the square of (m+x)/(n+x). In other words

m/n = ((m+x)/(n+x))^2

Let's isolate the term x^2 to get...

m/n = ((m+x)/(n+x))^2
m/n = ((m+x)^2)/((n+x)^2)
m(n+x)^2 = n(m+x)^2
m(n^2+nx+x^2) = n(m^2+mx+x^2)
mn^2+mnx+mx^2 = nm^2+mnx+nx^2
mn^2+mx^2 = nm^2+nx^2
mx^2-nx^2 = nm^2-mn^2
(m-n)x^2 = nm^2-mn^2
x^2 = (nm^2-mn^2)/(m-n)
x^2 = (mn(m-n))/(m-n)
x^2 = mn

RELATED QUESTIONS
If the random variable X has Hypergeometric distribution with parameters n, N and M,... (answered by textot)

A function f is defined for integers m and n as given: {{{ f(mn) =... (answered by Edwin McCravy)

A function f is defined for integers m and n as given: f(mn)=f(m)f(n)-f(m+n)+ 1001, where (answered by ikleyn)

if M and N are two matrices such that MN=N and NM=M show that M^2 + N^2= M +... (answered by richard1234)

can u help me on this hehe i need 3 examples of every law of exponents(FIRST TO FOURTH... (answered by josgarithmetic)

can you help me on this hehe i need 3 examples of every law of exponents(FIRST TO FOURTH... (answered by Solver92311)

can u help me on this hehe i need 3 examples of every law of exponents(FIRST TO FOURTH... (answered by Solver92311)

Algebra please show me an example of how to figure out the answer to this algebra... (answered by ewatrrr)

If {{{a^m*a^n}}}={{{a^mn}}},then... (answered by Alan3354)