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**segfault****Member**- Registered: 2019-01-10
- Posts: 2

The expression given is ∛(7 + 5√2), which is to be expressed in the form x + y√2. The answer given in the back of the book is 1 + √2, which is indeed numerically the same as ∛(7 + 5√2), but I'm damned if I can see how you get from one to the other. Any suggestions? Thanks in advance!

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Hi segfault,

Welcome to the forum!

Suppose that there are some values x and y for which ∛(7 + 5√2) = x + y√2. What happens if you cube both sides of that equation?

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**segfault****Member**- Registered: 2019-01-10
- Posts: 2

Hi zetafunc,

I see where you're going with this, expanding (x + y√2)^3 gives x^3 + 3√2x^2y + 6xy^2 + 2√2y^3 = 7 + 5√2

Now if I substitute x = 1 and y = 1 on the LHS I do get the RHS, and this gives 1 + √2 as required, but is there a more systematic way to find the values of x and y?

It reminds me of the technique of using undetermined coefficients in partial fractions, but not sure how to do it in this case...

Thanks again.

*Last edited by segfault (2019-01-10 22:20:47)*

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