Question

6 minus 4 route 2 by 6 plus 4 route 2

Answer 1

$\frac{6 - 4\sqrt{2}}{6 + 4\sqrt{2}} = \frac{(6 - 4\sqrt{2})(6 - 4\sqrt{2})}{(6 + 4\sqrt{2})(6 - 4\sqrt{2})} = \frac{(6 - 4\sqrt{2})^2}{6^2 - (4\sqrt{2})^2} = \frac{36 + 32 - 48\sqrt{2}}{36 - 32} = \frac{36 + 32 - 48\sqrt{2}}{4} \\ \\ = \frac{4(9 + 8 - 12\sqrt{2})}{4} \\ \\ = 9 + 8 - 12\sqrt{2} \\ \\ = 3^2 + (2\sqrt{2})^2 - (2 * 3 * 2\sqrt{2}) \\ \\ = (3 - 2\sqrt{2})^2$

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Answer 2

The answer is 5 by 1, which is equal to 5