Thread: prove that
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Old September 7th, 2008, 07:06 PM
sportsfan93b sportsfan93b is offline
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Quote:
Originally Posted by Soroban View Post
Hello, perash!

I got the first half . . .


I happened to notice that: .\begin{array}{ccc}3 + 12\sqrt[3]{11} - 6\sqrt[3]{121} &=& \left(\sqrt[3]{11} - 2\right)^3 \\ \\[-3mm] 16 -27\sqrt[3]{11} + 9\sqrt[3]{121} &=& \left(3 - \sqrt[3]{11}\right)^3 \end{array}


(a) Therefore: .A + B \;=\;\sqrt[3]{\left(\sqrt[3]{11}-2\right)^3} + \sqrt[3]{\left(3-\sqrt[3]{11}\right)^3} \;=\;\left(\sqrt[3]{11} - 2\right) + \left(3 - \sqrt[3]{11}\right) \;=\;1
In your final solution wouldnt the cube route and the 3rd pwr cancel out?
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