# 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
4 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.

- 4 years, 6 months ago

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

- 4 years, 6 months ago