Question

Va rog ajutatima
|3√2-2√5|+2×|1-2√5|

Answer 1

|3V2-2V5|=2V5-3V2
|1-2V5|=2V5-1
2V5-3V2+2x(2V5-1)
2V5-3V2+4V5-2 = 6V5-3V2-2  

Answer 2

$|3\sqrt 2 -2 \sqrt 5| + 2|1-2\sqrt 5| \\ \\ \dfrac{3\sqrt 2}{2\sqrt 5} = \dfrac{\sqrt{3^2\cdot 2}}{\sqrt{2^2\cdot 5}} = \dfrac{\sqrt{18}}{\sqrt{20}} < 1 \Rightarrow 3\sqrt 2 < 2\sqrt 5 \Rightarrow 3\sqrt 2 - 2\sqrt 5 <0 \\ \\ \Rightarrow |3\sqrt 2 - 2\sqrt 5| = 2\sqrt 5 - 3\sqrt 2\\ \\ \\ \dfrac{1}{2\sqrt 5} = \dfrac{\sqrt 1}{\sqrt {20}} <1 \Rightarrow 1 <2\sqrt 5 \Rightarrow 1 - 2\sqrt 5 < 0 \Rightarrow |1-2\sqrt 5 | = 2\sqrt 5 -1$

$\Rightarrow 2\sqrt 5 - 3\sqrt 2 + 2\cdot (2\sqrt 5 - 1) = 6\sqrt 5 - 3\sqrt 2 - 2$