Difference of squares: If sqrt{x + 15} + sqrt{x} = 15, find the value of x.

[Concor]

My main trouble is with two points in this solution. The first is the middle part where [math](\sqrt{x + 15}- \sqrt{x } \times 15 = 15[/math] appears and i don't now how or why. Also i don't know why the +1 in the 15+1 is there in the last part of the solution. All help is greatly appreciated.

 

[khansaheb]

View attachment 36949View attachment 36950

My main trouble is with two points in this solution. The first is the middle part where [math](\sqrt{x + 15}- \sqrt{x } \times 15 = 15[/math] appears and i don't now how or why. Also i don't know why the +1 in the 15+1 is there in the last part of the solution. All help is greatly appreciated.

Let:
\(\displaystyle (\sqrt{x+15}) - \sqrt{x})\) = A ................................ and ...............................................................................................(1)

\(\displaystyle (\sqrt{x+15}) + \sqrt{x})\) = B ...........................Then from given problem statement B = 15 ......................(2)

It was shown that (using \(\displaystyle (m + n) * (m - n) =m^2 - n^2\))

\(\displaystyle (\sqrt{x+15}) - \sqrt{x}) * (\sqrt{x+15}) + \sqrt{x})\) = 15 .......................................................................................(3)

→ A * B = 15..........Then using (2) here we get

A * 15 = 15 → A = 1

I am "guessing" you are just staring at the "screen" and not using pencil and paper. Please write the steps on the paper and follow...........

If you still fail to understand, let us know.