Question

Determinati numerele rationale a si b:

$2a(\sqrt{3} - \sqrt{5}) - 3b(2\sqrt{3} + \sqrt{5}) = \sqrt{300} - \sqrt{5}$

Answer 1

Răspuns:

$2a\sqrt{3} -2a\sqrt{5} -6b\sqrt{3} -3b\sqrt{5} =10\sqrt{3} -\sqrt{5} \\(2a-6b)\sqrt{3} -(2a+3b)\sqrt{5} =10\sqrt{3} -\sqrt{5} \\\\2a-6b=10\\2a+3b=1\\-9b=9\\b=-1\\a-3(-1)=5\\a+3=5\\a=5-3\\a=2$

Explicație pas cu pas: