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anonymous

  • 5 years ago

I don't understand the underlined step

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  1. anonymous
    • 5 years ago
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    Please open the attachment for details

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  2. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    Ack, sorry I missed something in the first step.

  4. anonymous
    • 5 years ago
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    We are given that \(\sqrt{a} + \sqrt{b} = \sqrt{c} + \sqrt{d}\)

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spraguer (Moderator)
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