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Can anyone solve this problem

sqrt(38-12 sqrt(10)) transform into a sqrt 5 + b sqrt 2 where a and b is an integer

Note by Farahani Ibrahim 3 years, 11 months ago

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Let \(\sqrt{38-12\sqrt{10}}=a\cdot \sqrt{5} + b \cdot \sqrt{2}\)

\( \\ 38-12\sqrt{10}=5a^2+2b^2+2ab\)

Compare both sides to get \(ab=-6\), \(5a^2+2b^2=38\).

Now use the factors of \(-6\) to obtain \(a=2, b=-3\), the only solution.

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The solution is only one? Not (+-) 3?

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TopNewestLet \(\sqrt{38-12\sqrt{10}}=a\cdot \sqrt{5} + b \cdot \sqrt{2}\)

\( \\ 38-12\sqrt{10}=5a^2+2b^2+2ab\)

Compare both sides to get \(ab=-6\), \(5a^2+2b^2=38\).

Now use the factors of \(-6\) to obtain \(a=2, b=-3\), the only solution.

Log in to reply

The solution is only one? Not (+-) 3?

Log in to reply