1) ОДЗ :
x² - 5x + 6 > 0
(x - 2)(x - 3) > 0
+ - +
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2 3
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x ∈ (- ∞ ; 2) ∪ (3 ; + ∞)
-1\\\\0<\frac{1}{2}<1\\\\x^{2}-5x+6<2\\\\x^{2}-5x+4<0\\\\(x-1)(x-4)<0" alt="log_{\frac{1}{2} }(x^{2}-5x+6)>-1\\\\0<\frac{1}{2}<1\\\\x^{2}-5x+6<2\\\\x^{2}-5x+4<0\\\\(x-1)(x-4)<0" align="absmiddle" class="latex-formula">
+ - +
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1 4
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Ответ : x ∈ (1 ; 2) ∪ (3 ; 4)
![2)(\sqrt{15-4\sqrt{14} }-\sqrt{15+4\sqrt{14} })^{2}=15-4\sqrt{14}-2\sqrt{(15-4\sqrt{14})(15+4\sqrt{14})}+15+4\sqrt{14}=30-2\sqrt{225-224}=30-2=28\\\\\sqrt{15-4\sqrt{14} }-\sqrt{15+4\sqrt{14} }=\sqrt{28}=|2\sqrt{7}| 2)(\sqrt{15-4\sqrt{14} }-\sqrt{15+4\sqrt{14} })^{2}=15-4\sqrt{14}-2\sqrt{(15-4\sqrt{14})(15+4\sqrt{14})}+15+4\sqrt{14}=30-2\sqrt{225-224}=30-2=28\\\\\sqrt{15-4\sqrt{14} }-\sqrt{15+4\sqrt{14} }=\sqrt{28}=|2\sqrt{7}|](https://tex.z-dn.net/?f=2%29%28%5Csqrt%7B15-4%5Csqrt%7B14%7D%20%7D-%5Csqrt%7B15%2B4%5Csqrt%7B14%7D%20%7D%29%5E%7B2%7D%3D15-4%5Csqrt%7B14%7D-2%5Csqrt%7B%2815-4%5Csqrt%7B14%7D%29%2815%2B4%5Csqrt%7B14%7D%29%7D%2B15%2B4%5Csqrt%7B14%7D%3D30-2%5Csqrt%7B225-224%7D%3D30-2%3D28%5C%5C%5C%5C%5Csqrt%7B15-4%5Csqrt%7B14%7D%20%7D-%5Csqrt%7B15%2B4%5Csqrt%7B14%7D%20%7D%3D%5Csqrt%7B28%7D%3D%7C2%5Csqrt%7B7%7D%7C)