2. Tentukan bentuk paling sederhana dari a. (√3+√7)(√3-√7)/ 2√5-4√2 =
b. 3√3/√2+√7 =
c. √2-√3/√2+√3 =![]()
b. 3√3/√2+√7 =
c. √2-√3/√2+√3 =
Jawab:
Penjelasan dengan langkah-langkah:
[tex]a. \frac{(\sqrt{3}+\sqrt{7})(\sqrt{3}-\sqrt{7})}{2\sqrt{5}-4\sqrt{2}}\\ \\=\frac{3-7}{2\sqrt{5}-4\sqrt{2}}\\ \\=\frac{-4}{2\sqrt{5}-4\sqrt{2}}\times\frac{2\sqrt{5}+4\sqrt{2}}{2\sqrt{5}+4\sqrt{2}}\\ \\=\frac{-4(2\sqrt{5}+4\sqrt{2})}{4.5-16.2}\\ \\=\frac{-4(2\sqrt{5}+4\sqrt{2})}{-12}\\ \\=\frac{1}{3}(2\sqrt{5}+4\sqrt{2})\\ \\ \\b.\frac{3\sqrt{3}}{\sqrt{2}+\sqrt{7}}\times\frac{\sqrt{2}-\sqrt{7}}{\sqrt{2}-\sqrt{7}}\\ \\=\frac{3\sqrt{6}-3\sqrt{21}}{2-7}\\ \\=\frac{3\sqrt{6}-3\sqrt{21}}{-5}[/tex]
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