Question

I don't understand the underlined step

Answer 1

Please open the attachment for details

Answer 2

We are given that (a+b) = (c+d).
If that is true, then (a+b)^2 must equal (c+d)^2.
But that means that \(a + 2\sqrt{ab} + b = c + 2\sqrt{cd} + d\)
And since a+b = c+d we can subtract those terms from both side to get that
\[\sqrt{ab} = \sqrt{cd}\]
Now we look at:
\[(\sqrt{a}-\sqrt{b})^2 = a -2\sqrt{ab} + b\]
\[(\sqrt{c}-\sqrt{d})^2 = c -2\sqrt{cd} + d\]

But here again, a+b = c+d, and \(\sqrt{ab} = \sqrt{cd}\)
So we can see that the two equations are equal and therefore

\[(\sqrt{a}-\sqrt{b})^2 =(\sqrt{c}-\sqrt{d})^2\]

Answer 3

Ack, sorry I missed something in the first step.

Answer 4

We are given that \(\sqrt{a} + \sqrt{b} = \sqrt{c} + \sqrt{d}\)