## anonymous 5 years ago I don't understand the underlined step

1. anonymous

Please open the attachment for details

2. anonymous

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

3. anonymous

Ack, sorry I missed something in the first step.

4. anonymous

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