Question

Demonstrati ca numarul a=4radical5 x (radical5+3radical20)-radical2(8-3radical18)+8radical2-148

Pun coroana!
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Answer 1

 

$\displaystyle\bf\\a=4\sqrt{5}\Big(\sqrt{5}+3\sqrt{20}\Big)-\sqrt{2}\Big(8-3\sqrt{18}\Big)+8\sqrt{2}-148\\\\a=4\sqrt{5}\Big(\sqrt{5}+3\sqrt{4\times5}\Big)-\sqrt{2}\Big(8-3\sqrt{9\times2}\Big)+8\sqrt{2}-148\\\\a=4\sqrt{5}\Big(\sqrt{5}+3\times2\sqrt{5}\Big)-\sqrt{2}\Big(8-3\times3\sqrt{2}\Big)+8\sqrt{2}-148\\\\a=4\sqrt{5}\Big(\sqrt{5}+6\sqrt{5}\Big)-\sqrt{2}\Big(8-9\sqrt{2}\Big)+8\sqrt{2}-148\\\\a=4\times5+4\times6\times5-8\sqrt{2}+9\times2+8\sqrt{2}-148$

.

$\displaystyle\bf\\a=20+120-\underline{8\sqrt{2}}+18+\underline{8\sqrt{2}}-148\\\\a=20+120+18-148\\\\a = 158-148\\\\\boxed{\bf~a=10\in N}$