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Mathematics

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, 6 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. Aditya Parson · 3 years, 6 months ago

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@Aditya Parson The solution is only one? Not (+-) 3? Farahani Ibrahim · 3 years, 5 months ago

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