Proof, please?

Today my friend gave me a formula which: a+2bc=b+c\sqrt{a+2\sqrt{bc}} = \sqrt{b} + \sqrt{c} Where b+c=ab+c=a. Can you give me the proof? She got it from her teacher, yet she didn't ask how her teacher got the formula.

#Proofs

Note by Kenny Indrajaya
7 years, 4 months ago

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Comments

Square both sides, you'll end up with a = b + c

Michael Mendrin - 7 years, 4 months ago

a+2bc \sqrt{ a + 2\sqrt{bc}}

=b+c+2bc = \sqrt{b + c + 2\sqrt{bc}}

=(b)2+(c)2+2bc = \sqrt{ (\sqrt{b})^2 + (\sqrt{c})^2 + 2\sqrt{bc}}

=(b+c)2 = \sqrt{ (\sqrt{b} + \sqrt{c})^2 }

=b+c = \sqrt{b} + \sqrt{c}

Siddhartha Srivastava - 7 years, 4 months ago

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thanks for this!

Kenny Indrajaya - 7 years, 4 months ago
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